1. 3-1 Graphing Systems of Equations
Hubarth
Algebra II

2. Ex 1 Solving a System of Equation
Solve by graphing. Check your solution.
y = 2x + 1
y = 3x – 1
Graph both equations on the same coordinate plane.
y = 2x + 1 The slope is 2. The y-intercept is 1.
y = 3x – 1 The slope is 3. The y-intercept is –1.
The lines intersect at (2, 5), so (2, 5) is the solution of the system.

3. . Ex 2 Solve system by Graphing Solve by Graphing y = 2x – 3 y = x – 1
(2, 1)
y = 2x – 3
m = 2
y-int = (0, -3)
y = x – 1
m = 1
y-int = (0, -1)
The lines intersect at (2, 1), so (2, 1) is the solution of the system.

4. Ex 3 Systems With No Solution
Solve by graphing. y = 3x + 2
y = 3x – 2
Graph both equations on the same coordinate plane.
y = 3x – 2 The slope is 3. The y-intercept is –2.
y = 3x + 2 The slope is 3. The y-intercept is 2.
The two lines have the same slope, different intercepts.
The lines are parallel. There is no solution.

5. Ex 4 Systems With Many Solutions
Solve by graphing. 3x + 4y = 12
y = − x + 3
Graph both equations on the same coordinate plane.
3x + 4y = 12 The y-intercept is 3.
The x-intercept is 4.
y = – x + 3 The slope is – . The y-intercept is 3. 3 4
The graphs are the same line. There are many solutions of ordered pairs (x, y), such that
y = – x + 3. 3 4

6. Practice
(-1, 5)
1. Solve the system by graphing.
y = 2x + 7
y = x + 6
y = 2x + 7
m = 2
y-int= (0, 7)
y = x + 6
m = 1
y-int = (0, 6)
2. Solve the system by graphing.
y = 4
x = -1
(-1, 4)
y = 4
x = -1
3. Solve the system by graphing.
y = -2x +1
y = -2x – 3
y = -2x + 1
m = -2
y-int = (0, 1)
y = -2x – 3
m = -2
y-int = (0, -3)
No solutions, the
lines are parallel.