Substitution With Two Variables

AJ was asked to find the solution to this system of equations. x = 7 - 2y 2x + y = 5 Noticing that x was isolated and set equal to 7 - 2y, he decided to replace x in the second equation with its value. What method is AJ using and what equation did he write?

• Elimination; 2(7-2y) + y = 5

• Graphing; 2x = (7-2y) + y = 5

• Substitution; 2(7-2y) + y = 5

• Substitution; x = 7 - 2y + 2x + y = 5

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Kayla solved the following system and found the solution to be (10, -9). x = -3y - 17 2x + 3y = -7 What would the graph of this system look like?

• A point on the coordinate plane

• Parallel Lines

• Coincident Lines (lines that graph one on top of the other)

• Lines that intersect at one point

Solve the system by using the substitution method

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Solve the system of equations using the substitution method

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

What is the second step to solve a system with substitution?

• Substitute the values found from the previous step into one of the original equations and solve for the remaining variable

• Solve the linear system for both its variables

• Solve one equation for one of its variables

• Substitute the expression from the previous step in the other two equations to obtain a linear system in two variables

The solution to the system of linear equations is...

Select all the methods you can use to solve a system of equations

• Graphing

• Elimination

• Substitution

• Using a Table

• Desmos