Math Word Problems Demystified - A Self Teaching Guide

In other words, in order to solve a system of equations, it is necessary to

find a value forxand a value forywhich, when substituted in the equations,

makes them both true.

There are several ways to solve a system of equations. The method used

here is called thesubstitutionmethod. You can use these steps:

Step 1: Select one equation and solve it for one variable in terms of the

other variable.

Step 2: Substitute this expression for the variable in theotherequation

and solve it for the remaining variable.

Step 3: Select one of the equations, substitute the value for the variable

found in Step 2, and solve for the other variable.

EXAMPLE:Solve the system

x
y¼ 3

2 xþy¼ 12

SOLUTION:

Step 1: Select the first equation and solve it forxin terms ofy.

x
y¼ 3

x
yþy¼ 3 þy

x¼ 3 þy

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

2 xþy¼ 12

2 ð 3 þyÞþy¼ 12

6 þ 2 yþy¼ 12

6 þ 3 y¼ 12

6 
 6 þ 3 y¼ 12 
 6

3 y¼ 6

31 y

31

¼

6

3

y¼ 2

198 REFRESHER V Systems of Equations