SOLUTION: 2x - y = -5 x + 3y =22 I have trouble solving this problem with Matrix. I have seen many examples in homework but this one has me beat as simple as it looks. Thanks, Enid

Algebra ->  Matrices-and-determiminant -> SOLUTION: 2x - y = -5 x + 3y =22 I have trouble solving this problem with Matrix. I have seen many examples in homework but this one has me beat as simple as it looks. Thanks, Enid      Log On


   

Question 249070: 2x - y = -5
x + 3y =22
I have trouble solving this problem with Matrix. I have seen many examples in homework but this one has me beat as simple as it looks.
Thanks, Enid
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1) Convert the system

system%282x+-+y+=+-5%2Cx+%2B+3y+=22%29


into the augmented matrix


%28matrix%282%2C3%2C2%2C-1%2C-5%2C1%2C3%2C22%29%29


Take note that the coefficients form the first 2x2 block and the right hand values form the last column. Visually, the correspondence is


---->

This conversion of notation allows us to ignore the variables (for now) since everything is based off of the numerical coefficients and right hand values.


Step 2) Row Reduction

Our next step is to row reduce the matrix %28matrix%282%2C3%2C2%2C-1%2C-5%2C1%2C3%2C22%29%29 into row reduced echelon form (rref form). (Note: Solution provided by the Linear Algebra Toolkit)



Looking at the last matrix %28matrix%282%2C3%2C1%2C0%2C1%2C0%2C1%2C7%29%29, the last column has the values 1 and 7 in it. So this means that the solution is x=1 and y=7 forming the ordered pair (1,7).