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Solving systems of equations

1. Solve by substitution or elimination method:
3x - 2y = 8
-12x + 8y = 32
2. Solve by substitution or elimination method:
7x - 5y = 14
-4x + y = 27
3. Solve by substitution or elimination method:
-4x + 3y = 5
12x - 9y = -15
4. A university bookstore recently sold a wire bound graph-paper notebook for $2.50 and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks was sold for a total of $118.60. How many of each type were sold?

5. Write a system of equations for each of the following, and solve each of the systems.

i. A unique solution.
ii. An infinite number of solutions.
iii. No solution.

Solution Preview

1. Solve by substitution or elimination method:
3x - 2y = 8 (1)
-12x + 8y = 32 (2)
(1)*(-4): - 12x + 8y = -32 (3)
(3) + (2): 0 = 0
thus, (1) is equivalent to (2), there are infinite solutions.

2. Solve by substitution or elimination method:
7x - 5y = 14 (1)
-4x + y = 27 (2)
from (2): y = 4x+27 substitute into (1):
7x - 5(4x+27) = 14
7x-20x-135 = 14
-13x = 149
x = -149/13 = -11.46
then y = 4x+27= 4(-11.46)+27 = ...

Solution Summary

This shows how to solve systems of equations using substitution or elimination.

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