Pre-Calculus: 1.7 Systems of Equations
Name __________________
Solve each system of equations.
1.
6 x  2 y  26
6 x  5 y  38
2.
4 x  3 y  28
9 x  y  6
3.
0.4x  0.1 y  0.25
12 x  3 y  7
4.
5 x  10 y  20
4 x  8 y  16
5.
3 x  y  2 z  2
x  2 y  2z  7
2 x  y  z  4
6.
7 x  12 y  13 z  3
3 x  4 y  5 z  21
11x  8 y  6 z  59
1. Label your equations (#1, #2, and #3)!
2. Reduce the 3 by 3 system to a 2 by 2 system:
a. Use two of the original equations to eliminate one variable (label this new
equation as #4)
b. Use a different pair of the original equations and eliminate the same
variable as before (label this new equation as #5)
c. Now you have a 2 by 2 system (equations #4 and #5) that you know how
to solve: solve it!
3. Substitute the values for the two variables into one of the original three equations
and find the value of the final variable. Then you’re done!
Example – Solve the following system of equations:
5 x  2 y  3 z  7
2 x  3 y  z  16
3x  4 y  2 z  7
#1
#2
#3
Reduce the 3 by 3 system to a 2 by 2 system. Use #1 and #3 to eliminate y.
#1
#3
5 x  2 y  3z  7
3x  4 y  2 z  7
2 ( 5 x  2 y  3z  7 )
3x  4 y  2 z  7
10 x  4 y  6 z  14
3x  4 y  2 z  7
13x
 8z  7
#4
8 x  12 y  4 z  64
9 x  12 y  6 z  21
17 x
 2z  43
#5
Use equations #2 and #3 to eliminate y again:
#2
#3
2 x  3 y  z  16
3x  4 y  2 z  7
4 ( 2 x  3 y  z  16 )
3 ( 3x  4 y  2 z  7 )
Create a 2 by 2 system using equations #4 and #5. Solve it!
#4
#5
13x  8z  7
17 x  2z  43
#4
13x  8z  7
13(3)  8 z  7
 39  8z  7
13x  8z  7
–4 ( 17 x  2z  43 )
13x  8z  7
 68x  8z  172
 55x
 165
x  3
z  4
Substitue the values for x and z into one of the original 3 equations to solve for y.
#2
2 x  3 y  z  16
2(3)  3 y  (4)  16
So, the solution is x  3, y  2, z  4
y2