# 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.

https://brainmass.com/math/linear-algebra/solving-systems-of-equations-29253

#### 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.