Let's solve a system by GRAPHING. Put the steps in order from first to last.

Solve both equations for y to get slope-intercept form

Graph both lines using the slope and y-intercept

The intersection point is the solution

First Steps for Solving Equations

Quiz

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.C.8B, HSA.REI.C.9, 7.EE.B.4A

+1

Standards-aligned

Anthony Clark

FREE Resource

10 questions

Show all answers

1.

DRAG AND DROP QUESTION

1 min • 5 pts

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

9-3y

y

12

-6

14y

x

10y

x+3y

24y

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

2.

DRAG AND DROP QUESTION

1 min • 2 pts

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

-42

3

30

-3

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

3.

DRAG AND DROP QUESTION

1 min • 5 pts

In this system
x+3y=9
4x-2y=-6
we have figured out that x=9-3y, and y=3.
Complete the steps to solve for x:
x=9-3( (a) )
x=9- (b)
x= (c)
The solution to the system is ( (d) , (e) ).

3

9

0

y

x

y=3

3y

-9

18

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

4.

REORDER QUESTION

1 min • 5 pts

Put the steps for solving by ELIMINATION in order:

Make sure the equations are lined up

Solve for the remaining variable

Subtract the equations to eliminate one variable

Plug that number into either original equation and solve for the other variable

Multiply one or both equations by a number to get common but opposite coefficients

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

5.

DRAG AND DROP QUESTION

1 min • 3 pts

Consider the system
4x+3y=-1
5x+4y=1
Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?
LCM = (a)
Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.
(b) (4x+3y=-1)
(c) (5x+4y=1)

12

4

-3

3

5

1

-1

-12

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

6.

DRAG AND DROP QUESTION

1 min • 5 pts

Consider the system
4x+3y=-1
5x+4y=1
After we do this multiplication, what will the new equations be?
4(4x+3y=-1) ---> (a) x + (b) y= (c)
-3(5x+4y=1) ---> (d) x - (e) y= -3

16

12

-4

-15

3

5

1

-1

-12

-3

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

7.

DRAG AND DROP QUESTION

1 min • 4 pts

Consider the system:
4x+3y=-1
5x+4y=1
Which we converted to:
16 x + 12y=-4
-15x - 12y= -3
Combining the equations straight down gives us:
(a) x+ (b) y= (c)
Solving for x, we get x= (d)

1

0

-7

3

5

-1

-12

-3

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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First Steps for Solving Equations

10 questions

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

In this system
x+3y=9
4x-2y=-6
we have figured out that x=9-3y, and y=3.
Complete the steps to solve for x:
x=9-3( (a) )
x=9- (b)
x= (c)
The solution to the system is ( (d) , (e) ).

Put the steps for solving by ELIMINATION in order:

Consider the system
4x+3y=-1
5x+4y=1
Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?
LCM = (a)
Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.
(b) (4x+3y=-1)
(c) (5x+4y=1)

Consider the system
4x+3y=-1
5x+4y=1
After we do this multiplication, what will the new equations be?
4(4x+3y=-1) ---> (a) x + (b) y= (c)
-3(5x+4y=1) ---> (d) x - (e) y= -3

Consider the system:
4x+3y=-1
5x+4y=1
Which we converted to:
16 x + 12y=-4
-15x - 12y= -3
Combining the equations straight down gives us:
(a) x+ (b) y= (c)
Solving for x, we get x= (d)

Consider the system:
4x+3y=-1
5x+4y=1
Since we now know that x=-7, solve for y:
4( (a) )+3y=-1
(b) +3y=-1
(c) = (d)
y= (e)

Let's solve a system by GRAPHING. Put the steps in order from first to last.

Solve for b:
-11 + 3(b + 5) = 7

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First Steps for Solving Equations

10 questions

In this systemx+3y=94x-2y=-6it'll be easiest to start by solving the first equation for x.The result of doing so is x=​9-3y.Fill in the blanks to plug that expression in and solve for y:4(​ (a) )-2​ (b) =-636-​ (c) y-2y=​ (d) 36-​ (e) =-6

In this systemx+3y=94x-2y=-6it'll be easiest to start by solving the first equation for x.The result of doing so is x=​9-3y.Fill in the blanks to plug that expression in and solve for y:4(​9-3y)-2​y =-636-​12y-2y=​-636-​14y =-6-14y=​ (a) y=​ (b)

In this systemx+3y=94x-2y=-6we have figured out that x=9-3y, and y=3.Complete the steps to solve for x:x=9-3(​ (a) )x=9-​ (b) x=​ (c) The solution to the system is (​ (d) ,​ (e) ).

Put the steps for solving by ELIMINATION in order:

Consider the system4x+3y=-15x+4y=1Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?LCM = ​ (a) Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.​ (b) (4x+3y=-1)​ (c) (5x+4y=1)

Consider the system4x+3y=-15x+4y=1After we do this multiplication, what will the new equations be?​ 4(4x+3y=-1) ---> ​ (a) x +​ (b) y=​ (c) ​-3(5x+4y=1)​ ---> ​ (d) x -​ (e) y= -3

Consider the system:4x+3y=-15x+4y=1Which we converted to:16 x +​ 12y=​-4-15x -​ 12y= -3Combining the equations straight down gives us:​ (a) x+​ (b) y=​ (c) Solving for x, we get x=​ (d)

Consider the system:4x+3y=-15x+4y=1Since we now know that x=-7, solve for y:4(​ (a) )+3y=-1​ (b) +3y=-1​ (c) =​ (d) y=​ (e)

Let's solve a system by GRAPHING. Put the steps in order from first to last.

Solve for b:-11 + 3(b + 5) = 7

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Discover more resources for Mathematics

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

In this system
x+3y=9
4x-2y=-6
we have figured out that x=9-3y, and y=3.
Complete the steps to solve for x:
x=9-3( (a) )
x=9- (b)
x= (c)
The solution to the system is ( (d) , (e) ).

Consider the system
4x+3y=-1
5x+4y=1
Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?
LCM = (a)
Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.
(b) (4x+3y=-1)
(c) (5x+4y=1)

Consider the system
4x+3y=-1
5x+4y=1
After we do this multiplication, what will the new equations be?
4(4x+3y=-1) ---> (a) x + (b) y= (c)
-3(5x+4y=1) ---> (d) x - (e) y= -3

Consider the system:
4x+3y=-1
5x+4y=1
Which we converted to:
16 x + 12y=-4
-15x - 12y= -3
Combining the equations straight down gives us:
(a) x+ (b) y= (c)
Solving for x, we get x= (d)

Consider the system:
4x+3y=-1
5x+4y=1
Since we now know that x=-7, solve for y:
4( (a) )+3y=-1
(b) +3y=-1
(c) = (d)
y= (e)

Solve for b:
-11 + 3(b + 5) = 7