Review for Systems of Equations Substitution Method

Rewrite the bottom equation after using substitution. Do not solve the system.

Mathematical Equivalence

ON

Solve the system of equations by using the Substitution Method.

y = 2x - 4

7x - 2y = 5

• (-1, -6)

• (-1, -8)

• (-2, 6)

• (1, -8),

Which answer has a correct next step for this system? (Read all three answers carefully before selecting one!)

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute 3x + 5 in the first equation like this:

  3x + 4(3x + 5) = 3

• The variable is already isolated for y, so we substitute 3x + 5 in the second equation like this:

  3(3x + 5) + 4y = 3

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Solve the following systems of equations using substitution:

5x - 2y = 3

y = 2x

• (6, 3)

• (1, 2)

• (3, 6)

• (2, 1)

Which answer has a correct first step for this system:

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the first equation and solve for x

  3x + 3(3x + 5) = 3

• Free sha vaca doo

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

• Make sure both equations can be solved.

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)