1. Warm Up Check to see if the point is a solution for the
system of linear equations.
1) 3x + 2y = ) x + y = -2
–x + 3y = x + 3y = -3
(2, -1) (-3, 1)
Find the solution for each graphed system.

2. 5.2 Solving Linear Systems by Substitution
EQ: How can you use substitution to solve a
systems of linear equations?
Rules for Solving Systems by Substitution:
1. Solve one of the equations for x or y.
2. In the other equation, substitute for the variable you
solved for and solve.
3. Substitute the number back into one of the
equations to solve for the other variable.

3. In the 1st equation, one variable is already solved (by itself).
Example 1:
y = 4x
x + y = 5
Solve by substitution
In the 1st equation, one variable
is already solved (by itself).
x = 5
So, substitute the 1st equation
in to the 2nd where the y is. 4x
5x = 5
Solve for x.
Now, substitute this back in to the
original 2nd equation and solve for y.
x = 1

4. y = 4 x
x + y = 5
x = 1
(1)
Substitute the x value in to the other
equation and solve for y.
y = 4
y = 4
The solution is (1, 4).

5. Solve by Substitution
3. y = x - 1
x + y = 3
4. 3x + 2y = -12
y = x - 1
2. x = -4
3x + 2y = 20
2. (-4, 16)
3. (2, 1)
4. (-2, -3)

6. Solve by Substitution
5. x = 1/2 y - 3
4x - y = 10
6. x = -5y + 4
3x + 15y = -1
7. 2x - 5y = 29
x = -4y + 8
5. (8, 22)
6. No solution
7. (12, -1)

7. Solve by Substitution
8. x =5y + 10
2x - 10y = 20
9. 4x + y = 0
x + 2y = -7
10. 2x - 3y = -24
x + 6y = 18
8. Many solutions
9. (1, -4)
10. (-6, 4)

8. Classwork/ Homework
Worksheet 8.1 & 8.2-all