SOLUTION: hi, i really need help with this. find the numerator for the y variable when using cramer's rule to solve x-3y=8 and 2x+2y=8. thanks a bunch!!

Algebra ->  Matrices-and-determiminant -> SOLUTION: hi, i really need help with this. find the numerator for the y variable when using cramer's rule to solve x-3y=8 and 2x+2y=8. thanks a bunch!!      Log On


   

Question 109445This question is from textbook algebra2 with trigonometry
: hi, i really need help with this. find the numerator for the y variable when using cramer's rule to solve x-3y=8 and 2x+2y=8. thanks a bunch!! This question is from textbook algebra2 with trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First set up a coefficient matrix:

A=%28matrix%282%2C2%2C1%2C-3%2C2%2C2%29%29

Now find the determinant of the matrix

det%28A%29=%282%2A1-2%2A-3%29=2%2B6=8

So to find the y solution, simply replace the second column of the coefficient matrix with the column %28matrix%282%2C1%2C8%2C8%29%29 to get the new matrix

B=%28matrix%282%2C2%2C1%2C8%2C2%2C8%29%29


Now find the determinant of this new matrix

det%28B%29=%281%2A8-2%2A8%29=8-16=-8


Now divide the determinant of B by the determinant of A to get


det%28B%29%2Fdet%28A%29=-8%2F8=-1

So the solution for y is -1 (ie y=-1)