Question

What are matrix A, matrix X, and matrix C for the system of linear equations -10x-3y=-2 and 4x+5y=16? How do I even begin to figure this out?

Answer 1

Given some system of equations
\[\begin{cases}ax+by=c\\
dx+ey=f\end{cases}\]
You can write it as a matrix equation \(AX=C\), where \(A\) is the matrix of coefficients, \(X\) is the coefficient of variables, and \(C\) is a constant matrix:
\[A=\begin{bmatrix}a&b\\d&e\end{bmatrix}\\
X=\begin{bmatrix}x\\y\end{bmatrix}\\
C=\begin{bmatrix}c\\f\end{bmatrix}\]

Answer 2

@SithsAndGiggles thank you! so X would be \[X= \left[\begin{matrix}-10 & -3 \\ 4 & 5\end{matrix}\right]\] C would be \[C= \left(\begin{matrix}-2 \\ 16\end{matrix}\right)\] and what would X be since there is two x's and y's?

Answer 3

\[\color{red}{A}= \left[\begin{matrix}-10 & -3 \\ 4 & 5\end{matrix}\right]\]
but yeah that's right.

Answer 4

yeah thats what I meant lol thank you!