Download 5. - Cincinnati Public Schools

5.2 Solving System of Equations Using
Substitution
Objectives:
-- To solve systems of equations algebraically
using the substitution method
Substitution Method
This method allows you to find exact solutions to systems.
1. Solve one of the equations of the system for one of the variables.
(It doesn’t matter which variable you solve for)
2.
Substitute that expression into the other equation, replacing the
variable that you solved for
3.
This leaves an equation with one variable
4.
Solve this equation for the variable to get its value
5
Take that value and substitute it back into one of the ORIGINAL
equations of the system to find the value of the second variable
6. Check to make sure that the ordered pair works in BOTH equations
of the system
Solve
d  0.2  50t

d  60t
Examples
when a system has both
equations solved for the same
variable, set the two expressions equal to each
other.
0.2  50t  60t one variable, solve for it
50t  50t
_____________
0.2  10t divide both sides by 10
0.02  t substitute into one of
the originals to find d
d  60(0.02)
The solution is (0.02, 1.2)
d  1.2
Solve
 x  y  90

0.05 x  0.2 y  9
Solve
2 x  2 y  4

x  3y  1
Solve
 y  4  3x

 y  2x 1