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High School Math : Solving Equations

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Example Questions

Example Question #214 : Algebra Ii

Solve:

2x-3y=13

x+3y=-7

Possible Answers:

(5,2)

(2,3)

(2,-3)

(3,-2)

(-3,5)

Correct answer:

(2,-3)

Explanation:

Add the two equations together to get 3x=6 . Then divide by to get x=2 .

Now substitute this value into one of the original equations to get 2+3y=-7 .

Next subtract from both sides to get 3y=-9 .

Now divide both sides by to get y=-3 .

Therefore the answer is (2,-3) .

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Example Question #27 : Equations

Lilac paint is made by mixing one part blue paint and one part red pain with two parts white paint. How many gallons of white paint should be mixed with two quarts of blue paint?

Possible Answers:

$0.75\; gallon$

$0.50\; gallon$

$1.00\; gallon$

$1.50\; gallons$

$1.25\; gallons$

Correct answer:

$1.00\; gallon$

Explanation:

Set up a proportion where number of quarts of white paint.

$\frac{white}{blue} = \frac{x\; qt}{2\; qt}= \frac{2}{1}$ and solve by cross multiplying to get $x=4\; quarts$ , and $4 \; quarts = 1\; gallon$ .

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Example Question #21 : Solving Equations

What number is $125\%$ of 160 ?

Possible Answers:

200

240

225

185

300

Correct answer:

200

Explanation:

For percentage problems look for verbal cues:

"IS" means equals.

"OF" means multiplication.

Therefore the equation becomes n=1.25(160)=200 .

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Example Question #22 : Equations

An art show wants to focus on sculpture but will also accept paintings and drawings. The show has room for 140 pieces and will display them in a ratio of scupltures to painting to drawings. How many sculptures will be displayed?

Possible Answers:

Correct answer:

Explanation:

Since the paintings and the drawings have the same ratio, they will have the same number on display.

Let number of paintings displayed = number of drawings displayed.

Then, 140 - 2x = number of sculptures displayed.

Set up a proportion:

$\frac{sculptures}{drawings}=\frac{140 - 2x}{x}=\frac{3}{2}$

Solve by cross multiplying to get 2(140-2x)=3x or 280 - 4x = 3x .

Then add to both sides to get 280 = 7x .

Then divide by to get x=40 .

So there are drawings and paintings in the show, leaving the last spots for sculptures.

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Example Question #22 : Solving Equations

What number is $125\%$ of 240 ?

Possible Answers:

300

325

340

365

285

Correct answer:

300

Explanation:

Verbal cues include "IS" means equal and "OF" means multiplication.

So the equation to solve becomes $n=1.25\cdot 240=300$

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Example Question #23 : Solving Equations

is what percent of ?

Possible Answers:

Correct answer:

Explanation:

Verbal cues include "IS" means equals and "OF" means multiplication.

So the equation to solve becomes

$15=P\cdot 75$ and dividing both sides by gives $P=0.20 \; or \; 20\%$

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Example Question #23 : Solving Equations

Solve the system of equations.

4x+y=16

2x+3y=18

Possible Answers:

(4,3)

(-4,3)

(3,4)

None of the other answers are correct.

(-3,4)

Correct answer:

(3,4)

Explanation:

Isolate in the first equation.

y=16-4x

Plug into the second equation to solve for .

2x+3(16-4x)=18

2x+48-12x=18

-10x+48=30

-10x=-30

x=3

Plug into the first equation to solve for .

4(3)+y=16

12+y=16

y=4

Now we have both the and values and can express them as a point: (3,4) .

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Example Question #4 : Solving Equations

Solve for and .

3x+2y=2

2x+2y=4

Possible Answers:

$x=2\ and\ y=-8$

$x=-2\ and\ y=8$

$x=-2\ and\ y=4$

$x=2\ and\ y=-4$

Cannot be determined.

Correct answer:

$x=-2\ and\ y=4$

Explanation:

1st equation: 3x+2y=2

2nd equation: 2x+2y=4

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Plug the value of into either equation and solve for :

2(-2)+2y=4

-4+2y=4

2y=4+4

2y=8

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Example Question #31 : Equations

Solve for :

$\left | 5x + 39 \right | = 44$

Possible Answers:

$x = 16\frac{3}{5}$

$x = -1 \textrm{ or } x = 1$

$x = -16\frac{3}{5} \textrm{ or } x = 1$

$x = 1 \textrm{ or }x = 16\frac{3}{5}$

$x = -16\frac{3}{5} \textrm{ or }x = 16\frac{3}{5}$

Correct answer:

$x = -16\frac{3}{5} \textrm{ or } x = 1$

Explanation:

Rewrite $\left | 5x + 39 \right | = 44$ as a compound statement and solve each part separately:

$\left | 5x + 39 \right | = 44$

$5x + 39 = - 44 \textrm{ or }5x + 39 = 44$

5x + 39 = - 44

5x + 39 - 39 = - 44- 39

5x = - 83

$5x \div 5 = - 83 \div 5$

$x = -16\frac{3}{5}$

5x + 39 = 44

5x + 39 - 39 = 44- 39

5x = 5

$5x \div 5 =5 \div 5$

x = 1

Therefore the solution set is $\left \{-16\frac{3}{5}, 1 \right \}$ .

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Example Question #32 : Equations

Solve the following equation for :

3(x+2) = 4(x-3)

Possible Answers:

x = -9

x = -18

x = 18

x = -6

x = 2

Correct answer:

x = 18

Explanation:

3(x+2) = 4(x-3)

The first step in solving this equation is to distribute the 3 and the 4 through the parentheses:

$3\cdot x+3\cdot2 = 4\cdot x-4\cdot 3$

Simplify:

3x+6 = 4x-12

Now, we want to get like terms on the same sides of the equation. That is, all of the terms with an should be on one side, and those without an should be on the other. To do this, we first subtract from both sides:

3x+6 -4x= 4x-12-4x

Simplify:

-x+6 = -12

Now, we subtract 6 from both sides:

-x+6-6 = -12-6

-x = -18

x = 18

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High School Math : Solving Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #214 : Algebra Ii

Example Question #27 : Equations

Example Question #21 : Solving Equations

Example Question #22 : Equations

Example Question #22 : Solving Equations

Example Question #23 : Solving Equations

Example Question #23 : Solving Equations

Example Question #4 : Solving Equations

Example Question #31 : Equations

Example Question #32 : Equations

All High School Math Resources

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