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

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

Solve for the remaining variable

Subtract the equations to eliminate one variable

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