Math Word Problems Demystified - A Self Teaching Guide

Step 3: Selectx
y¼3, substitutey¼2 and solve forx.

x
y¼ 3

x
 2 ¼ 3

x
 2 þ 2 ¼ 3 þ 2

x¼ 5

Hence, the solution to the system isx¼5 andy¼2.

You can check the solution by substitutingx¼5 andy¼2 in the other

equation and seeing if it is true.

2 xþy¼ 12

2 ð 5 Þþ 2 ¼ 12

10 þ 2 ¼ 12

12 ¼ 12

EXAMPLE:Solve the system

xþ 3 y¼
 7

3 x
y¼ 9

SOLUTION:

Step 1: Solve the first equation forx.

xþ 3 y¼
 7

xþ 3 y
 3 y¼
 7 
 3 y

x¼
 7 
 3 y

Step 2: Substitute
 7 
 3 yin the second equation and solve fory.

3 x
y¼ 9

3 ð
 7 
 3 yÞ
y¼ 9

 21 
 9 y
y¼ 9

 21 
 10 y¼ 9

 21 þ 21 
 10 y¼ 9 þ 21

REFRESHER V Systems of Equations 199