1. Lesson 0 – 8 Systems of Linear Equations
Geometry
Lesson 0 – 8
Systems of Linear Equations
Objective:
Use graphing, substitution, and elimination to
solve systems of equations.

2. one solution (2, 1) y = -x + 3 y = 2x - 3
Solve by graphing, then state whether one solution, no solution, or infinitely many.
y = -x + 3
y = 2x - 3
one solution (2, 1)

3. Solve by graphing… y – 2x = 6 3y – 6x = 9 y = 2x + 6 y = 2x + 3
Easier to graph if you use
slope-intercept form.
y – 2x = 6
3y – 6x = 9
y = 2x + 6
y = 2x + 3
No solution

4. The equations are the same which means they
Solve by graphing
y = 3x + 1
2y = 6x + 2
Solve for y
y = 3x + 1
The equations are the same which means they
have the same graph.
Infinitely many solutions

5. Solve by substitution y = 5 3x = 5 y = 3x -2y + 9x = 5 -2(3x) + 9x = 5
Plug x back in to find y.
y = 3x
-2y + 9x = 5
-2(3x) + 9x = 5
y = 5
-6x + 9x = 5
3x = 5

6. Solve by substitution 2(-4x) + 3x = 8 -8x + 3x = 8 y = -4x 2y + 3x = 8
Plug x back in to find y.
y = -4x
2y + 3x = 8
2(-4x) + 3x = 8
-8x + 3x = 8
-5x = 8

7. Plug into either equation
Solve by Elimination
Plug into either equation
to find y.
3x + 2y = 7
4x + 2y = 0
4(-7) + 2y = 0
-x = 7
2y = 28
x = -7
y = 14
(-7, 14)

8. (-1, 2) Solve by Elimination 3x + 5y = 7 4x + 2y = 0 12x + 20y = 28
Pick which variable to eliminate.
(4)
3x + 5y = 7
4x + 2y = 0
(3)
12x + 20y = 28
12x + 6y = 0
Plug in to find other variable.
4x + 2(2) = 0
4x + 4 = 0
14y = 28
4x = -4
y = 2
x = -1
(-1, 2)

9. Homework
Pg. P18 1 – 15 all