We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 Next →

Example Question #21 : Systems Of Equations

The sum of the digits in a positive three-digit whole number is equal to 13. When the digits are reversed, the number's value is decreased by 594. If the first digit must be a prime number, then what is the sum of the squares of the three digits?

Possible Answers:

Correct answer:

Explanation:

Since the number has three digits, there must be a digit in the hundreds place, a digit in the tens place, and a digit in the ones place. Let's let h represent the digit in the hundreds place, t represent the digit in the tens place, and let u represent the digit in the ones place. Thus, we can represent our mystery number as follows:

mystery number = 100h + 10t + u

First, we are told that the sum of the digits is 13. Thus, we can write the following equation.

h + t + u = 13

Next, we are told that reversing the digits decreases the value of the original number by 594. We already established that the original number can be represented as 100h + 10t + u. We can then represent the reversed number as 100u + 10t + h. We can now write the following equation:

original number = 594 + reversed number

100h + 10t + u = 594 + 100u + 10t + h

Let's get the h, t, and u terms on the same side. Subtract h from both sides.

99h + 10t + u = 594 + 100u + 10t

Subtract 10t from both sides.

99h + u = 594 + 100u

Subtract 100u from both sides.

99h – 99u = 594

Since 99 and 594 are divisible by 9, we will divide both sides by 9.

11h – 11u = 66

Divide both sides by 11.

h – u = 6

We are told that the first digit, represented by h, must be prime. Let's solve for h in terms of u by adding u to both sides.

h = 6 + u

Since h is a digit, it can't be larger than 9. (The possible values for a digit are 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.) The only prime numbers less than 9 are 2, 3, 5, and 7. However, if h were 2, 3, or 5, then u would be negative, and we can't have a negative digit. In short, the only value that h can be is 7.

7 = 6 + u

Since h is 7, u must be 1.

If h = 7 and u = 1, we will solve for t by using the first equation h + t + u = 13.

7 + t + 1 = 13

Subtract 8 from both sides.

t = 5

Since h = 7, t = 5, and u = 1, the number must be 751. We are told to find the squares of the digits.

sum of squares of digits = 7² + 5² + 1² = 49 + 25 + 1 = 75.

The answer is 75.

Report an Error

Example Question #22 : Systems Of Equations

Given the following system of inequalities, find the answer below that does NOT satisfy the system.

$\dpi{80} x-y> 1$

$\dpi{80} 2x-3y< 6$

Possible Answers:

$\dpi{80} (1,-1)$

$\dpi{80} (2,0)$

$\dpi{80} (0,-1)$

$\dpi{80} (4,1)$

$\dpi{80} (3,1)$

Correct answer:

$\dpi{80} (0,-1)$

Explanation:

To be a solution to the system, the point must satisfy BOTH inequalities. All five points satisfy the inequality $\dpi{80} 2x-3y< 6$ . On the other hand, $\dpi{80} \left (0, -1)$ does not satisfy $\dpi{80} x-y> 1$ .

$\dpi{80} \left ( 0) - (-1)> 1?$

$\dpi{80} 0+1 > 1?$

$\dpi{80} 1> 1? (No)$

Report an Error

Example Question #231 : Equations / Inequalities

20 fifth graders attended a birthday party. Each child got to choose between playing minature golf, which cost $4, or bowling, which cost $6. The total cost of the party was $96. How many children playing minature golf?

Possible Answers:

Correct answer:

Explanation:

Let x equal the number of children that played minature golf and let y equal the number of children who bowled.

Based on that, we can conclude that:

$x + y =20$

and

$4x + 6y =96$

Let's solve for x in the first equation by subtracting y from each side. $20-y=x$

Now, let's substitute that expression for x in the second equation:

$4(20-y) + 6y = 96$

Now, distribute the 4:

$80-4y + 6y =96$

Simplify:

$80+2y=96$

Subtract 80 from both sides:

$2y=16$

Divide both sides by 2:

$y=8$

Therefore, 8 children bowled. By substituting y into the first equation, we know that $x+8=20$

Solve for x by subtracting 8 from both sides: $x=12$

Report an Error

Example Question #22 : How To Find The Solution For A System Of Equations

At what point will the lines $\dpi{100} \small 4x+2=y$ and $\dpi{100} \small 3x+3=y$ intersect?

Possible Answers:

(1, 6)

(6, 1)

(1, –6)

(6, –1)

(–1, 6)

Correct answer:

(1, 6)

Explanation:

In order to find this point, we must find the solution to the system of equations. we will use substitution, setting the two expressions for y equal to one another.

$\dpi{100} \small 4x+2=3x+3 \rightarrow x=1$

Then we plug this value back into either expression for y, giving us $\dpi{100} \small y=4\times 1+2=6$

So the point is (1, 6).

Report an Error

Example Question #25 : Systems Of Equations

Let $\dpi{100} A$ be the point of intersection between the lines given by the equations $\dpi{100} 2x-5y=4$ and $\dpi{100} 4x-7y=9$ . What is the slope of the line that passes through $\dpi{100} A$ and the origin?

Possible Answers:

$-\frac{17}{2}$

$\frac{2}{17}$

$\frac{17}{6}$

$-\frac{17}{6}$

$\frac{17}{2}$

Correct answer:

$\frac{2}{17}$

Explanation:

In order to solve this system of equations, it will probably be best to use the elimination method, in which we add or subtract two equations. In general, if $\dpi{100} a=b$ , and $\dpi{100} c=d$ , then $\dpi{100} a+c=b+d$ . In other words, we can combine equations.

We need to solve the following equations:

$2x-5y=4$

$4x-7y=9$

We want to look for a way to combine these two equations that will eliminate at least one variable. If, for example, we multiplied the first equation by $\dpi{100} -2$ and then added this to the second equation, we could get rid of the $\dpi{100} x$ terms. Let's multiply the first equation by $\dpi{100} -2$ . Remember, we must multiply both sides.

$-2(2x-5y)=(-2)(4)$

Distribute the $\dpi{100} -2$ .

$-4x+10y=-8$

We can now add $-4x+10y=-8$ to the equation $4x-7y=9$ . The sum of the left sides of each equation will equal the sum of the right sides.

$(-4x+10y)+(4x-7y)=-8+9$

We can simplify both sides. Notice that the $\dpi{100} x$ terms on the left disappear, leaving only $\dpi{100} y$ terms.

$3y = 1$

Divide both sides by 3.

$y=\frac{1}{3}$ .

Now that we have $\dpi{100} y$ , we can go back to either of our original two equations, substitute the value of $\dpi{100} y$ we obtained, and solve for $\dpi{100} x$ . Let's use the equation $2x-5y=4$ .

Substitute $\dpi{100} \frac{1}{3}$ for $\dpi{100} y$ .

$2x-5(\frac{1}{3})=4$

$2x-\frac{5}{3}=4$

Add $\dpi{100} \frac{5}{3}$ to both sides. We will need to rewrite 4 with a denominator of 3.

$2x = 4 + \frac{5}{3}=\frac{12}{3}+\frac{5}{3}=\frac{17}{3}$

Divide by 2 on both sides. When dividing a fraction, we simply multiply by its reciprocal.

$x = \frac{17}{3}\div 2=\frac{17}{3}\cdot \frac{1}{2}=\frac{17}{6}$

Point $\dpi{100} A$ , which is the intersection of the lines, must have the coordinates $\left ( \frac{17}{6},\frac{1}{3} \right )$ .

The question ultimately asks for the slope of the line passing through $\dpi{100} A$ and the origin. We can use the equation of the slope between two points with coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$ .

slope = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{\frac{1}{3}-0}{\frac{17}{6}-0}$

$= \frac{\frac{1}{3}}{\frac{17}{6}}$

$=\frac{1}{3}\div \frac{17}{6}=\frac{1}{3}\cdot \frac{6}{17}=\frac{2}{17}$

The answer is $\frac{2}{17}$ .

Report an Error

Example Question #26 : Systems Of Equations

Where do the lines $y=3x-6$ and $y=2x+5$ intersect?

Possible Answers:

(11,27)

(1,7)

(5,22)

(-4,13)

(22,5)

Correct answer:

(11,27)

Explanation:

Finding the intersection of two lines is the same as solving simultaneous equations. Here, both equations are already solved for , so the right sides of both equations are set equal to each other. Solving for results in a value of 11. Setting equal to 11 in either of the original equations gives a value of 27.

Report an Error

Example Question #27 : Systems Of Equations

At a carnival, hamburgers cost $4 while hot dogs cost $2. Becky has to buy 18 items for her students. She spent a total of $48. How many hamburgers did she buy?

Possible Answers:

Correct answer:

Explanation:

Let x equal the number of hamburgers and y equal the number of hotdogs.

$\small x+y=18$

$\small 4x+2y=48$

Solve for y in the first equation.

$\small y=18-x$

Substitute that solution into the second equation.

$\small 4x+2(18-x)=48$

$\small 4x+36-2x=48$

$\small 2x+36=48$

$\small 2x=12$

$\small x=6$

Report an Error

Example Question #23 : How To Find The Solution For A System Of Equations

This year, Amy is 3 times older than Jackie. In 6 years, Amy will be 2 times older than Jackie. How old is Jackie today?

Possible Answers:

Correct answer:

Explanation:

Let Amy's current age be equal to A and Jackie's age be equal to J.

Therefore, $\small A=3J$ and $\small (A+6)=2(J+6)$

Substitute the first equation into the second.

$\small (3J+6)=(2J+12)$

$\small J+6=12$

$\small J=6$

Therefore, today Jackie is 6 years old.

Report an Error

Example Question #29 : Systems Of Equations

Bobbie's Boots makes winter boots. Their monthly fixed expenses are $600. The cost for making a pair of boots is $35. The boots sell for $75 a pair.

What is the monthly break-even point?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal the revenue.

Costs: C(b)=600+35b

Revenue: R(b)=75b

So Costs = Revenue or 600+35b=75b

Solving for shows the break-even point is achieved when 15 pairs of boots are sold in a month.

Report an Error

Example Question #30 : Systems Of Equations

Bobbie's Boots makes winter boots. Their monthly fixed expenses are $600. The cost for making a pair of boots is $35. The boots sell for $75 a pair.

To make a profit of $200, how many pairs of boots must be sold?

Possible Answers:

Correct answer:

Explanation:

Profits = Revenue - Costs

Revenue: R(b)=75b

Costs: C(b)=600+35b

P(b)=R(b)-C(b)=75b-(600+35b)=40b-600

Solving:

200=40b-600

for means that 20 pairs of boots must be sold to make $200 profit.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 Next →

View SAT Mathematics Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

View SAT Mathematics Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in Phoenix, GRE Courses & Classes in Seattle, SAT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in New York City, GMAT Courses & Classes in Denver, SAT Courses & Classes in Seattle, LSAT Courses & Classes in Phoenix, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Phoenix, SAT Test Prep in Houston, MCAT Test Prep in Miami, GRE Test Prep in Washington DC, LSAT Test Prep in New York City, GRE Test Prep in Seattle, ACT Test Prep in Houston, MCAT Test Prep in Boston, GMAT Test Prep in Seattle

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SAT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Systems Of Equations

Example Question #22 : Systems Of Equations

Example Question #231 : Equations / Inequalities

Example Question #22 : How To Find The Solution For A System Of Equations

Example Question #25 : Systems Of Equations

Example Question #26 : Systems Of Equations

Example Question #27 : Systems Of Equations

Example Question #23 : How To Find The Solution For A System Of Equations

Example Question #29 : Systems Of Equations

Example Question #30 : Systems Of Equations

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: