# SOLVING SYSTEMS OF EQUATIONS GRAPHICALLY

## About "Solving systems of equations graphically"

Solving systems of equations graphically :

We can check whether the ordered pair (x, y) is a solution of an equation in two variables by substituting the x- and y-values into the equation.

When we substitute the x- and y-values into the equation, if it results a true statement, then (x, y) is a solution of an equation.

In the system of two equations, if a point lies on the graphs of both the equations, the point is a solution of both equations and is, therefore, a solution of the system.

## Solving systems of equations graphically - Examples

Example 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).

Example 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).

After having gone through the stuff given above, we hope that the students would have understood "Solving systems of equations graphically"

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