Substitution Equation 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

What is the number of solutions to the system of equations? (Notice there are two lines graphed one on top of the other.)

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

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

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Solve the system of equations using substitution:

-4x + 4y = 8

y = -2x - 10

• (-4, -2)

• (12, -34)

• (4, -18)

• (-2, -6)

• (-4, 6)

Solve for x and y (Use Substitution)

y = 2x + 1

y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

• (1,1)

If x = -3, in the equation -2x + y = 15, what is y? Type in the number.

Solve using Substitution Method

y = -6

-3x - 6y = 24

• (6, 6)

• (6, -6)

• (4, -6)

• (-6, 4)

x = y - 2
4x + y = 2

• (2,0)

• (0,2)

• (0, -2)

• (-2,0)

Solve the following system of equations: 5x - 4y = 3 and 2x + 3y = 8

• x = 4, y = 3

• x = 2, y = 1

• x = 3, y = 2

• x = 1, y = 5