# SOLVING SYSTEMS OF EQUATIONS GRAPHICALLY WORKSHEET

## About "Solving systems of equations graphically worksheet"

Solving systems of equations graphically worksheet :

Worksheet on solving systems of equations graphically is much useful to the students who would like to practice problems on solving system of linear equations in two variables.

## Solving systems of equations graphically worksheet - Problems

1.  Solve the given system of equations by graphing.

x + y - 4  =  0

3x - y  =  0

2.  Solve the given system of equations by graphing.

3x - y - 3  =  0

x - y - 3  =  0

## Solving systems of equations graphically worksheet - Solution

Problem 1 :

Solve the given system of equations by graphing.

x + y - 4  =  0

3x - y  =  0

Solution :

Step 1 :

Let us re-write the given equations in slope-intercept form  (y = mx + b).

y  =  - x + 4

(slope is -1 and y-intercept is 4)

y  =  3x

(slope is 3 and y-intercept is 0)

Based on slope and y-intercept, we can graph the given equations.

Step 2 :

Find the point of intersection of the two lines. It appears to be (1, 3). Substitute to check if it is a solution of both equations.

x + y - 4  =  0

1 + 3 - 4  =  0  ?

4 - 4  =  0  ?

0  =  0  True

3x - y  =  0

3(1) - 3  =  0  ?

3 - 3  =  0  ?

0  =  0  True

Since the point (1, 3) satisfies both the equations, the solution of the system is (1, 3).

Problem 2 :

Solve the given system of equations by graphing.

3x - y - 3  =  0

x - y - 3  =  0

Solution :

Step 1 :

Let us re-write the given equations in slope-intercept form.

y  =  3x - 3

(slope is 3 and y-intercept is -3)

y  =  x - 3

(slope is 1 and y-intercept is -3)

Based on slope and y-intercept, we can graph the given equations.

Step 2 :

Find the point of intersection of the two lines. It appears to be (0, -3). Substitute to check if it is a solution of both equations.

3x - y - 3  =  0

3(0) - (-3) - 3  =  0  ?

0 + 3 - 3  =  0  ?

0  =  0  True

x - y - 3  =  0

0 - (-3) - 3  =  0  ?

3 - 3  =  0  ?

0  =  0  True

Since the point (0, -3) satisfies both the equations, the solution of the system is (0, -3).

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