3.2 Solving Systems of Linear Equations Algebraically
There are several ways to solve a system of linear equations. We are going to look at two methods that serve as alternatives to graphing.
Substitution Method is best to use if one equation is solved for a variable OR is it is
“easy” to solve an equation for one variable.
1.) Solve one equation for a variable.
2.) Substitute this expression into the other equation for that variable.
3.) Solve the new equation that now has only one variable.
4.) Plug this value into an original equation and solve for the second variable.
5.) Check your answer by plugging both variables into the other original equation.
a)


 y
3 x
=
+
2 x
2 y
−
=
9
10
b)



3
− x
2 x
+
2
+ y y
=
=
1
4
c)



3 x x
+
2 y y
=
6
−
4
= −
12

d)
 3

 x x
− y
= y
4
−
9
+
3
= −
12
e)



−
2 x
+ y
=
4 x
−
2 y
=
6
5 f) Penncrest is planning a 5 hour outing at a local park. The park rents bicycles for $8 per hour and roller blades for $6 per hour. The total budget per person is $34. How many hours should students spend doing each activity? g) Your family is planning a 7 day trip to Florida. Mom estimated it will cost
$275 per day in Tampa and $400 per day in Orlando. The total budget for the trip is $2300. How many days should your family spend in each location?