2 x + 4 y = − 4 2x\ +\ 4y\ =\ -4 2 x + 4 y = − 4 − 2 x − 2 y = 4 -2x\ -\ 2y\ =\ 4\ \ \ \ \ \ \ − 2 x − 2 y = 4

( − 2 , 4 ) (-2,4) ( − 2 , 4 )

( − 2 , − 4 ) (-2,-4) ( − 2 , − 4 )

4 x + 4 y = 16 4x\ +\ 4y\ =\ 16 4 x + 4 y = 1 6 5 x + − 4 y = − 7 5x\ +\ -4y\ =\ -7 5 x + − 4 y = − 7

( − 3 , − 1 ) (-3,-1) ( − 3 , − 1 )

( − 1 , 3 ) (-1,3) ( − 1 , 3 )

− x − 3 y = − 7 -x\ -3y\ =\ -7 − x − 3 y = − 7 x + 2 y = 3 \ x\ +\ 2y\ =\ 3 x + 2 y = 3

( − 5 , 4 ) (-5,4) ( − 5 , 4 )

( − 4 , 6 ) (-4,6) ( − 4 , 6 )

( − 5 , − 1 ) (-5,-1) ( − 5 , − 1 )

x − 6 y = 14 \ x\ -\ 6y\ =\ 14 x − 6 y = 1 4 − x − 4 y = 16 -x\ -\ 4y\ =\ 16 − x − 4 y = 1 6

( − 4 , − 3 ) (-4,-3) ( − 4 , − 3 )

− 2 x + 4 y = 6 -2x\ +\ 4y\ =\ 6 − 2 x + 4 y = 6 − x − 4 y = 9 \ -x\ -\ 4y\ =\ 9 − x − 4 y = 9

( − 5 , − 1 ) (-5,-1) ( − 5 , − 1 )

( 5 , − 1 ) (5,-1) ( 5 , − 1 )

( − 1 , 5 ) (-1,5) ( − 1 , 5 )

4 x + 4 y = − 4 \ 4x\ +\ 4y\ =\ -4 4 x + 4 y = − 4 − 2 x − 4 y = − 2 -2x\ -4y\ =\ -2 − 2 x − 4 y = − 2

( − 3 , 2 ) (-3,2) ( − 3 , 2 )

( 2 , − 3 ) (2,-3) ( 2 , − 3 )

− 5 x + 3 y = 14 -5x\ +\ 3y\ =\ \ 14 − 5 x + 3 y = 1 4 x − 3 y = − 10 \ \ x\ -\ 3y\ =\ -10 x − 3 y = − 1 0

( − 1 , 3 ) (-1,3) ( − 1 , 3 )

( − 3 , 3 ) (-3,3) ( − 3 , 3 )

− 3 x + 2 y = 0 -3x\ +\ 2y\ =\ 0 − 3 x + 2 y = 0 − 2 x + 2 y = 0 -2x\ +\ 2y\ =\ 0 − 2 x + 2 y = 0

( 0 , − 4 ) (0,-4) ( 0 , − 4 )

− 2 x + 2 y = 18 -2x\ +\ 2y\ =18 − 2 x + 2 y = 1 8 2 x + 6 y = 6 \ 2x\ +\ 6y\ =\ \ 6 2 x + 6 y = 6

( − 6 , 3 ) \left(-6,3\right) ( − 6 , 3 )

( 6 , 3 ) \left(6,3\right) ( 6 , 3 )

( 6 , − 3 ) \left(6,-3\right) ( 6 , − 3 )

Parallel Lines never intersect because...

they have the same y-intercept.

they have different y-intercepts.

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

10c + 5d = 16.50 5c + 10d = 14.25

10c + 5d = 14.25 5c + 10d = 16.50

System of Equations

Authored by Adriana Latronica

Mathematics

8th Grade

CCSS covered

Used 2+ times

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34 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

No Solution

$(-2,4)$

$(-2,-4)$

$(6,4)$

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$4x\ +\ 4y\ =\ 16$
$5x\ +\ -4y\ =\ -7$

$(3,1)$

$(1,3)$

$(-3,-1)$

$(-1,3)$

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$5x\ +\ 4y\ =\ 5$
$6x\ -4y\ =6$

$(1,0)$

Infinite number of solutions

$(0,1)$

$(4,0)$

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$-x\ -3y\ =\ -7$
$\ x\ +\ 2y\ =\ 3$

$(6,4)$

$(-4,6)$

$(-5,4)$

$(-5,-1)$

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\ x\ -\ 6y\ =\ 14$
$-x\ -\ 4y\ =\ 16$

Infinite number of solutions

No Solution

$(4,3)$

$(-4,-3)$

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$-2x\ +\ 4y\ =\ 6$
$\ -x\ -\ 4y\ =\ 9$

$(-5,-1)$

$(5,-1)$

$(-1,5)$

$(1,5)$

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

$(-3,2)$

No Solution

$(3,2)$

$(2,-3)$

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$-5x\ +\ 3y\ =\ \ 14$

$\ \ x\ -\ 3y\ =\ -10$

No Solution

$(-1,3)$

$(-3,3)$

$(3,3)$

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$-3x\ +\ 2y\ =\ 0$
$-2x\ +\ 2y\ =\ 0$

No Solution

$(0,-4)$

$(0,0)$

$(4,0)$

Tags

CCSS.8.EE.C.8B

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$-2x\ +\ 2y\ =18$
$\ 2x\ +\ 6y\ =\ \ 6$

$\left(-6,3\right)$

$\left(6,3\right)$

$\left(6,-3\right)$

Infinite number of solutions

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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System of Equations

2x + 4y = −42x\ +\ 4y\ =\ -42x + 4y = −4 −2x − 2y = 4 -2x\ -\ 2y\ =\ 4\ \ \ \ \ \ \ −2x − 2y = 4

4x + 4y = 164x\ +\ 4y\ =\ 164x + 4y = 16 5x + −4y = −75x\ +\ -4y\ =\ -75x + −4y = −7

5x + 4y = 55x\ +\ 4y\ =\ 55x + 4y = 5 6x −4y =66x\ -4y\ =66x −4y =6

−x −3y = −7-x\ -3y\ =\ -7−x −3y = −7 x + 2y = 3\ x\ +\ 2y\ =\ 3 x + 2y = 3

x − 6y = 14\ x\ -\ 6y\ =\ 14 x − 6y = 14 −x − 4y = 16-x\ -\ 4y\ =\ 16−x − 4y = 16

−2x + 4y = 6-2x\ +\ 4y\ =\ 6−2x + 4y = 6 −x − 4y = 9\ -x\ -\ 4y\ =\ 9 −x − 4y = 9

4x + 4y = −4\ 4x\ +\ 4y\ =\ -4 4x + 4y = −4 −2x −4y = −2-2x\ -4y\ =\ -2−2x −4y = −2

−5x + 3y = 14-5x\ +\ 3y\ =\ \ 14−5x + 3y = 14 x − 3y = −10\ \ x\ -\ 3y\ =\ -10 x − 3y = −10

−3x + 2y = 0-3x\ +\ 2y\ =\ 0−3x + 2y = 0 −2x + 2y = 0-2x\ +\ 2y\ =\ 0−2x + 2y = 0

−2x + 2y =18-2x\ +\ 2y\ =18−2x + 2y =18 2x + 6y = 6\ 2x\ +\ 6y\ =\ \ 6 2x + 6y = 6

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

$4x\ +\ 4y\ =\ 16$
$5x\ +\ -4y\ =\ -7$

$5x\ +\ 4y\ =\ 5$
$6x\ -4y\ =6$

$-x\ -3y\ =\ -7$
$\ x\ +\ 2y\ =\ 3$

$\ x\ -\ 6y\ =\ 14$
$-x\ -\ 4y\ =\ 16$

$-2x\ +\ 4y\ =\ 6$
$\ -x\ -\ 4y\ =\ 9$

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

$-5x\ +\ 3y\ =\ \ 14$

$\ \ x\ -\ 3y\ =\ -10$

$-3x\ +\ 2y\ =\ 0$
$-2x\ +\ 2y\ =\ 0$

$-2x\ +\ 2y\ =18$
$\ 2x\ +\ 6y\ =\ \ 6$