# solve Matrices simultaneously

• March 1st 2010, 03:43 AM
decoy808
solve Matrices simultaneously
4x+3y=2
-x+7y=15

$\begin{bmatrix}{d11}{d12}&\\{d21}{d22}\end{bmatrix }$ . $\frac{x}{y}=\frac{b1}{b2}$

$\frac{x}{y}=\begin{bmatrix}{A}\end{bmatrix}^{-1}\frac{b1}{b2}$

$\begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}^{-1}\frac{2}{15}=\frac{x}{y}$

this is where im getin confused. do i need to find the inverse matrix then multiply out to get answer? im geting very big values(Worried)

many thanks
• March 1st 2010, 04:06 AM
sa-ri-ga-ma
Your method is correct. Proceed.
• March 1st 2010, 06:53 AM
HallsofIvy
However, writing $\frac{x}{y}$ makes it look like a fraction!

What you mean is
$\begin{bmatrix}4 & 3 \\ -1 & 7\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix} 2 \\ 15\end{bmatrix}$

so
$\begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix}4 & 3 \\ -1 & 7\end{bmatrix}^{-1}\begin{bmatrix} 2 \\ 16\end{bmatrix}$

Since the determinant of that is 4(7)- 3(-1)= 28+ 3= 31, you should NOT have very large numbers! You should have fractions with 31 in the denominator.