SOLUTION: I just need to solve the matrix-I do know the answer, however, I'm not sure of how to do the problem. 3x+4y=13 2x-3y=-14 the answer is (-1,4) Please help!

Algebra ->  Matrices-and-determiminant -> SOLUTION: I just need to solve the matrix-I do know the answer, however, I'm not sure of how to do the problem. 3x+4y=13 2x-3y=-14 the answer is (-1,4) Please help!      Log On


   

Question 114564This question is from textbook Algebra for College Students
: I just need to solve the matrix-I do know the answer, however, I'm not sure of how to do the problem.
3x+4y=13
2x-3y=-14
the answer is (-1,4)
Please help! This question is from textbook Algebra for College Students

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x+4y=13
2x-3y=-14
In matrix form, it would look like,

[A][x]=[b]
The solution is

Where k,l,m,n are coefficients of the inverse matrix of
%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29
[x]=[A%5E-1][b]
The inverse of a 2x2 matrix, A, where
[A]=%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++a%2C+b%2C%0D%0A+++c%2C+d%0D%0A+%29%0D%0A%29
is given by
[A%5E-1]=
Using your coefficients in the inverse matrix formula,
[A%5E-1]=
[A%5E-1]=
[A%5E-1]=
The solution is therefore

Let's carry out each calculation separately,
x=%281%2F17%29%2A%283%2813%29%2B%284%29%28-14%29%29
x=%281%2F17%29%2A%2839-56%29
x=%281%2F17%29%2A%28-17%29
highlight%28x=-1%29
y=%281%2F17%29%2A%282%2813%29%2B%28-3%29%28-14%29%29
y=%281%2F17%29%2A%2826%2B42%29
y=%281%2F17%29%2A%2868%29
highlight%28y=4%29