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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Equations / Solution Sets

What is the solution to the following system of equations:

3x+5y = 15

3x+3y = 15

Possible Answers:

$x=2,y=\frac{13}{4}$

x=3,y=2

$x=\frac{1}{3},y=3$

$x=3,y=\frac{6}{5}$

x = 5, y = 0

Correct answer:

x = 5, y = 0

Explanation:

By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

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Example Question #271 : Equations / Inequalities

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

$3\frac{1}{3}$

None of the other choices are correct.

$3\frac{2}{3}$

$2\frac{2}{3}$

Correct answer:

$3\frac{2}{3}$

Explanation:

Multiply the bottom equation by 5, then add to the top equation:

6x-y = 24

$5 \left (6x-y \right ) =5\cdot 24$

30x-5y =120

$\underline{\textrm{\; } 3x + 5y = \; \; 1}$

$33x \;\;\;\;\;\; \; =121$

$x = \frac{121}{33} = \frac{11}{3} = 3 \frac{2}{3}$

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Example Question #32 : Equations / Solution Sets

Solve this system of equations for :

3x + 5y = 23

6x-y = -9

Possible Answers:

$y = 2 \frac{1}{2}$

$y = 3 \frac{1}{2}$

None of the other choices are correct.

y = 3

y = 5

Correct answer:

y = 5

Explanation:

Multiply the top equation by :

3x + 5y = 23

$-2 \cdot \left (3x + 5y \right )= -2 \cdot 23$

$-6x -10y \right )= -46$

Now add:

$6x-\; \; y = -9$

$\underline{-6x -10y = -46}$

-11y = - 55

$-11y \div (-11) = -55\div (-11)$

y = 5

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Example Question #162 : Expressions & Equations

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

y = -2

$y = -1 \frac{4}{5}$

$y = -2 \frac{1}{5}$

None of the other choices are correct.

$y = -1 \frac{3}{5}$

Correct answer:

y = -2

Explanation:

Multiply the top equation by :

3x + 5y = 1

$-2 \cdot \left (3x + 5y \right )= -2 \cdot 1$

$-6x -10y \right )= -2$

Now add:

$\; \; 6x-\; \; \; y = 24$

$\underline{-6x -10y= -2} \right )$

-11y = 22

$-11y \div (-11) = 22\div (-11)$

y = -2

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Example Question #33 : Equations / Solution Sets

Find the solution to the following system of equations.

a + 3b = 5

a-2b = 0

Possible Answers:

$a = 1,\ b = 1$

$a = 1,\ b = 2$

$a = 2,\ b = 2$

$a = 2,\ b = 3$

$a = 2,\ b = 1$

Correct answer:

$a = 2,\ b = 1$

Explanation:

a + 3b = 5

a-2b = 0

To solve this system of equations, use substitution. First, convert the second equation to isolate $\small a$ .

$a-2b = 0\rightarrow a=2b$

Then, substitute $\small 2b$ into the first equation for $\small a$ .

a + 3b = 5

(2b) + 3b = 5

Combine terms and solve for $\small b$ .

5b=5

b=1

Now that we know the value of $\small b$ , we can solve for $\small a$ using our previous substitution equation.

a=2b=2(1)=2

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Example Question #34 : Equations / Solution Sets

Find a solution for the following system of equations:

$\left\{\begin{matrix} x-2y-1=3\\ -x+2y+2=5 \end{matrix}\right.$

Possible Answers:

infinitely many solutions

$\left ( 4,0 \right )$

no solution

$\left ( 8,2 \right )$

Correct answer:

no solution

Explanation:

When we add the two equations, the and variables cancel leaving us with:

1=8 which means there is no solution for this system.

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Example Question #12 : How To Find The Solution For A System Of Equations

Solve the set of equations:

3x+2y=12

4x-3y=-1

Possible Answers:

$\left ( -1,-1 \right )$

$\left ( 1,1 \right )$

$\left ( 2,3 \right )$

$\left ( 4,0 \right )$

Correct answer:

$\left ( 2,3 \right )$

Explanation:

Solve the first equation for :

3x+2y=12

2y=12-3x

$y=6-\frac{3}{2}x$

Substitute into the second equation:

$4x-3(6-\frac{3}{2}x)=-1$

$4x-18+\frac{9}{2}x=-1$

Multiply the entire equation by 2 to eliminate the fraction:

8x-36+9x=-2

17x-36=-2

17x=34

x=2

Using the value of , solve for :

3(2)+2y=12

6+2y=12

2y=6

y=3

Therefore, the solution is $\left ( 2,3 \right )$

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Example Question #161 : Systems Of Equations

Solve the following system of equations:

y = 2x-2

y = 3x+6

Possible Answers:

x=-4,y=-10

x=8,y=14

x=4,y=16

x=-4,y=-6

x=-8, y=-18

Correct answer:

x=-8, y=-18

Explanation:

Set the two equations equal to one another:

2x - 2 = 3x + 6

Solve for x:

x = -8

Plug this value of x into either equation to solve for y. We'll use the top equation, but either will work.

y = 2 * (-8) - 2

y = -18

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Example Question #51 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

3x + 5y = 23

6x-y = -9

Possible Answers:

$\frac{1}{3}$

$-\frac{2}{3}$

None of the other choices are correct.

$-\frac{1}{3}$

$\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Multiply the bottom equation by , then add to the top equation:

6x-y = -9

$5 \left (6x-y \right ) =5\cdot (-9)$

30x-5y = -45

$\underline{\textrm{\; } 3x + 5y = \; \; 23}$

$33x \;\;\;\;\;\; \; =-22$

Divide both sides by

$\frac{33x}{33}=-\frac{22}{33}$

$\frac{22}{33}=-\frac{2}{3}$

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Example Question #52 : How To Find The Solution For A System Of Equations

Solve the following system of equations:

$\left\{\begin{matrix} 4x-2y=-3\\ 4x+2y=-5 \end{matrix}\right.$

Possible Answers:

$\left(-1,-\frac{1}{2} \right )$

$\left(\frac{1}{2}, -4\right)$

infinitely many solutions

no solution

Correct answer:

$\left(-1,-\frac{1}{2} \right )$

Explanation:

When we add the two equations, the variables cancel leaving us with:

8x=-8

Solving for we get:

$\frac{8x}{8}=\frac{-8}{8}$

x=-1

We can then substitute our value for into one of the original equations and solve for :

$\begin{matrix} -4-2y=-3\\ -4+4-2y=-3+4\\ -2y=1\\ y=-\frac{1}{2}\\ \end{matrix}$

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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #31 : Equations / Solution Sets

Example Question #271 : Equations / Inequalities

Example Question #32 : Equations / Solution Sets

Example Question #162 : Expressions & Equations

Example Question #33 : Equations / Solution Sets

Example Question #34 : Equations / Solution Sets

Example Question #12 : How To Find The Solution For A System Of Equations

Example Question #161 : Systems Of Equations

Example Question #51 : How To Find The Solution For A System Of Equations

Example Question #52 : How To Find The Solution For A System Of Equations

All Common Core: 8th Grade Math Resources

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