Easy Algebra Step-by-Step

Systems of Equations 211

Solution

Step 1. Write both equations in slope-intercept form.

The fi rst equation, 2x + 5 y = 3, yields yx+

2

5

3

5

.

The second equation, 3x − 2y = 1, yields yxx−

3

2

1

2

.

Step 2. Graph both equations on the same graph.

1

–1

–2

2

y

x

y =^3

2

x –^1

2

y = –2

5

x+^3

5

–2

You can fi nd an approximate solution of x ≈ 0.579 and y ≈ 0.368 by using a

graphing utility. These values are close estimates but will not exactly satisfy

either equation. Of course, you can fi nd the exact solution of x=

11

19

and

y=

7

19

by using either the substitution method or the elimination method.

Nevertheless, the graphical approach gives you the

approximate location of the intercept (if any), and,

more important, this method helps you see the con-

nection between the solution and the graphs of the

two equations.

When an exact solution is

needed, do not use the graphing

method for solving a system of

equations.