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
xy¼ 3
2 xþy¼ 12
SOLUTION:
Step 1: Select the first equation and solve it forxin terms ofy.
xy¼ 3
xyþy¼ 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