Question

Solve the system.

2y = 4x + 2
2y = -x + 7

Answer 1

with matrices

Answer 2

well

Answer 3

2y = 4x + 2
2y = -x + 7
Thus, 4x + 2 = -x + 7
4x + x = 7 - 2
5x = 5
x = 1
Put x = 1 into any of the two equations
2y = 4(1) + 2
2y = 4 + 2
2y = 6
y = 3
Therefore (x, y) = (1, 3)

Answer 4

WITH matrices.

Answer 5

\[\left[\begin{matrix}-4 & 2 \\ 1 & 2\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}2 \\ 7\end{matrix}\right)\]
\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \left[\begin{matrix}-4 & 2 \\ 1 & 2\end{matrix}\right]^{-1} \left(\begin{matrix}2 \\ 7\end{matrix}\right)\]

Answer 6

\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -4(2) -2(1) }\left[\begin{matrix}2 & -2 \\ -1 & -4\end{matrix}\right]\left(\begin{matrix}2 \\ 7\end{matrix}\right)\]

Answer 7

\[\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}\left[\begin{matrix}2 & -2 \\ -1 & -4\end{matrix}\right]\left(\begin{matrix}2 \\ 7\end{matrix}\right)\]\]

Answer 8

\[\[\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}]\left(\begin{matrix}4 - 14 \\ -2 - 28\end{matrix}\right)\]\]\]

Answer 9

\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}]\left(\begin{matrix}- 10 \\ -30\end{matrix}\right) = \left(\begin{matrix}1 \\ 3\end{matrix}\right)\]