Solving Systems Substitution/Elimination Test

What order is the 5 steps for elimination method?

• Determine which variable to eliminate

• Plug variable back into equation

• Place in Standard Form

• Check your solution

• Add or subtract the equations

What are the five steps to solving systems using substitution method.

• Substitute

• Solve the equation

• Solve an equation for one variable

• Check your solution

• Plug back in to find the other variable

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=​

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)-2​y =-6

36-​12y-2y=​-6

36-​14y =-6

-14y=​ (a)  

y=​ (b)  

• -42
• 3
• 30
• -3

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

Put the steps for solving by ELIMINATION in order:

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

• Subtract the equations to eliminate one variable

• Make sure the equations are lined up

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

• Solve for the remaining variable

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

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

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

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)  

• -7
• -28
• 3y
• 27
• 9
• 5
• 7
• -12
• 3
• y