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Common Core: 8th Grade Math : Expressions & Equations

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

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #8 : Understand That The Solution Of A System Of Two Linear Equations Is The Intersection Of Their Lines: Ccss.Math.Content.8.Ee.C.8a

Identify the point of intersection by solving for the solution of the system of equations in the provided figure.

Possible Answers:

(0,8)

(-3,4)

(-8,4)

(-9,12)

(-10,5)

Correct answer:

(-8,4)

Explanation:

The graph displays a system of two linear equations. The point where these two lines intersect is the solution to the system of the equations because that coordinate point is the point that both lines have in common, or pass through.

In this case, the solution to the two linear equations that are displayed in the graph is the following point:

(-8,4)

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Example Question #161 : Expressions & Equations

Identify the point of intersection by solving for the solution of the system of equations in the provided figure.

Possible Answers:

(8,-8)

(-8,8)

(9,-9)

(-9,9)

(-9,-9)

Correct answer:

(-9,-9)

Explanation:

In this case, the solution to the two linear equations that are displayed in the graph is the following point:

(-9,-9)

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Example Question #162 : Expressions & Equations

Identify the point of intersection by solving for the solution of the system of equations graphed in the provided figure.

Possible Answers:

(-12,3)

(-11,5)

(14,-7)

(-14,7)

(7,-5)

Correct answer:

(-11,5)

Explanation:

In this case, the solution to the two linear equations that are displayed in the graph is the following point:

(-11,5)

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Example Question #1 : How To Find The Solution For A System Of Equations

3x + y = 8

2x + 4y = 12

Solve the system for and .

Possible Answers:

x = 2, y = 2

x = 10, y = -2

x = 3, y = -1

x = 2, y = 0

x = -4, y = 20

Correct answer:

x = 2, y = 2

Explanation:

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply 3x + y = 8 by (-4) to get -12x - 4y = -32 .

Then, we can add 2x + 4y = 12 to this equation to yield -10x = -20 , so x = 2 .

We can plug that value into either of the original equations; for example, 3(2) )+ y = 8 .

So, y = 2 as well.

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Example Question #1 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

What is the solution to the following system of equations:

3x+5y = 15

3x+3y = 15

Possible Answers:

x=3,y=2

x = 5, y = 0

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

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

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

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 #3 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

None of the other choices are correct.

$3\frac{1}{3}$

$2\frac{2}{3}$

$3\frac{2}{3}$

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 #2 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Solve this system of equations for :

3x + 5y = 23

6x-y = -9

Possible Answers:

y = 5

None of the other choices are correct.

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

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

y = 3

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 #3 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

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

y = -2

None of the other choices are correct.

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

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

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 #151 : Systems Of Equations

Find the solution to the following system of equations.

a + 3b = 5

a-2b = 0

Possible Answers:

$a = 1,\ b = 2$

$a = 2,\ b = 1$

$a = 2,\ b = 2$

$a = 1,\ b = 1$

$a = 2,\ b = 3$

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 #5 : How To Find The Solution For A System Of Equations

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:

$\left ( 8,2 \right )$

$\left ( 4,0 \right )$

no solution

infinitely many solutions

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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Common Core: 8th Grade Math : Expressions & Equations

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #8 : Understand That The Solution Of A System Of Two Linear Equations Is The Intersection Of Their Lines: Ccss.Math.Content.8.Ee.C.8a

Example Question #161 : Expressions & Equations

Example Question #162 : Expressions & Equations

Example Question #1 : How To Find The Solution For A System Of Equations

Example Question #1 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Example Question #3 : How To Find The Solution For A System Of Equations

Example Question #2 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Example Question #3 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Example Question #151 : Systems Of Equations

Example Question #5 : How To Find The Solution For A System Of Equations

All Common Core: 8th Grade Math Resources

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