Download Solving Systems of Equations by Substitution

Math 10C
Systems of Linear Equations: Lesson #2
Solving Systems of Equations by Substitution
Objective: By the end of this lesson, you will be able to:
Warm-Up:
 For each equation, substitute the given value for x into the second equation and solve for y:
a) x  1 , 3x  4 y  6
b) x  y  2 , 2 x  3 y  6
Systems of equations can be solved algebraically rather than by graphing. One way to do this is
to use the method of _____________________.
1. Choose one equation and ________________ one of the variables.
2. _________________ the expression from step 1 into the other equation. (Notice that this
equation now only has one variable.)
3. Solve the equation.
4. Substitute the value you got in step 3 into ___________ of the original equations to solve
for the other variable.
e.g. 1) Solve each system by substitution:
y  5 x  13
a)
(Check the solution by replacing the solution in the original equations.)
7 x  y  35
Math 10C
Systems of Linear Equations: Lesson #2
b)
m  n  4
4m  6n  9
3x  6 y   12
c) x
y3
5
e.g. 2) Admission to the 2009 Abbotsford Airshow cost $80 for a car with two adults and three
children. Admission for a car with two adults cost $50. Write a system of equations to
model this situation and then solve it by substitution to determine the cost per child and
the cost per adult. (There is no charge for the vehicle; just a cost per child and per adult.)
Assignment:
p. 425-426 #4-5, 8, 19