Systems of EquationsSolving by Graphing

Systems of Equations

• One way to solve equations that involve two different variables is by graphing the lines of both equations on a coordinate plane.

• If the two lines cross the solution for both variables is the coordinate of the point where they intersect.

y = 2x + 0 & y = -1x + 3

Slope = 2/1y-intercept= 0

Up 2 and

right 1

y-intercept= +3

Slope = 1/-1

Up 1 and

left 1The solution is the point they cross at (1,2)

(1,2)

y = x - 3 & y = -3x + 1

Slope = 1/1y-intercept= -3

y-intercept= +1

Slope = 3/-1

The solution is the point they cross at (1,-2)

Graph y = x -3 y = x + 2

Solution= none

NUMBER OF SOLUTIONS OF A LINEAR SYSTEM

IDENTIFYING THE NUMBER OF SOLUTIONS

y

x

y

x

Lines intersectone solution

Lines are parallelno solution

y

x

Lines coincideinfinitely many solutions

Name the Solution

Name the Solution

Name the Solution

Systems of EquationsSolving by Graphing