matrix equation problem O__O?

Question

ok i need help using matrices to solve this system of equations
please try to show work as i pretty much thought i knew this but aparently i dont

2.7x - 3.5y=13.35
6.3x + 4y= 12.9

omg this stuff sucks.

Answer 1

That equation is just the following when written as a matrix (// = new line)
[ 2.7 -3.5 // 6.3 4][x // y] = [13.35 // 12.9]
Now, you need to find the inverse of the left hand matrix. The inverse of [a b // c d] is 1/(ad-bc) * [d -b // -c a].
So, the inverse is 1/32.85 * [4 3.5 // -6.3 2.7].
So, multiplying both sides by that:
[x // y ] = 1/32.85 * [4 3.5 // -6.3 2.7][13.35 // 12.9].
Multiplying that out gives [x // y] = [3 // -1.5]

Answer 2

The matrix form of those equation is C*[x,y]=[13.35, 12.9]. It is difficult to show column vectors here, so interpret [x,y] as the x,y column vector (x over y) and [13.35,12.9] as another column vector, then C is the square coefficient matrix. The soulution is

[x,y] = C(inverse) * [13.35, 12.9]

I assume you know how to multiply matrices and vectors, and how to find the inverse of a matrix. You can find help here http://en.wikipedia.org/wiki/Matrix_%28mathematics%29
and http://en.wikipedia.org/wiki/Matrix_%28mathematics%29
and http://en.wikipedia.org/wiki/System_of_linear_equations