Systems of Equations Solving by Graphing Systems of Equations One way to solve equations that involve two different variables is by graphing the lines.

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