Question

Explain, complete sentences, the process of using Cramer’s Rule to solve the following system of equations. Provide the solution to the system.

8x + 3y = 14
12x + 4y = 17

Answer 1

Set up one determinant for D and one for Dy. The values for determinant D are taken from the coefficients of the system (8 and 3 in row 1, 12 and 4 in row 2):
D=
|8 3|
|12 4|
Dy is set up the same way, but substitute the constants (14 and 17) for the coefficients of y in the determinant:
Dy=
|8 14|
|12 17|
Solve the determinants:
D=
|a b|
|c d|
Dy=
|a e|
|c f|
D is solved by (a)(d)-(b)(c); and Dy is solved by (a)(f)-(e)(c)
D= (8)(4)-(3)(12) = 32 - 36 = -2
Dy= (8)(17)-(14)(12) = 136 - 168 = -32
y=Dy/D
y=-32/-2 = 16

Answer 2

Thank you, I figured out what I was doing wrong.