Steps to Solve a System of Equations

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

• The intersection point is the solution

• Solve both equations for y to get slope-intercept form

• Graph both lines using the slope and y-intercept

Put the steps for solving by SUBSTITUTION in order:

• Plug the resulting expression into the other equation

• Solve for the second variable

• Plug that number into the other equation

• Solve for the first variable

• Solve one equation for x or y

In this system x+3y=9 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

Put the steps for solving by ELIMINATION in order:

• Subtract the equations to eliminate one variable

• Solve for the remaining 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

• Make sure the equations are lined up

Solve the system.

• No Solution

• Infinitely Many Solutions

• (2, -1, 5)

• (3, -2, 1)

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(​ (a)   )-2​ (b)   =-6

36-​ (c)   y-2y=​ (d)  

36-​ (e)   =-6

• 9-3y

• y

• 12

• -6

• 14y

• x

• 10y

• x+3y

• 24y

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

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

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