Math Word Problems Demystified - A Self Teaching Guide

 10 y¼ 30

 101 y


 101

¼

30

10

y¼
 3

Step 3: Substitute
3 foryin the first equation and find the value forx.

xþ 3 y¼
 7

xþ 3 ð
 3 Þ¼
 7

x
 9 ¼
 7

x
 9 þ 9 ¼
 7 þ 9

x¼ 2

You can check the solution by using 3x
y¼9 whenx¼2 andy¼
3.

3 x
y¼ 9

3 ð 2 Þ
ð
 3 Þ¼ 9

6 þ 3 ¼ 9

9 ¼ 9

When selecting an equation and a variable to solve for in Step 1, you

should look for an equation which has a variable whose numerical coefficient

is one. Since this is not always possible, you still can use the substitution

method to solve the equation as shown in the next example.

EXAMPLE:Solve the system

5 x
 7 y¼
 31

4 xþ 3 y¼ 1

SOLUTION:

Step 1: Select the second equation and solve fory.

200 REFRESHER V Systems of Equations