To solve the system of equations:
[tex]\[
\begin{cases}
-2x + 5y = 4 \\
2x - 4y = -2 \\
\end{cases}
\][/tex]
we can use matrices and the method of solving systems of linear equations using matrix operations.
First, represent the system of equations in matrix form [tex]\( A\mathbf{x} = \mathbf{b} \)[/tex], where:
[tex]\[
A = \begin{pmatrix}
-2 & 5 \\
2 & -4
\end{pmatrix}, \quad
\mathbf{x} = \begin{pmatrix}
x \\
y
\end{pmatrix}, \quad
\mathbf{b} = \begin{pmatrix}
4 \\
-2
\end{pmatrix}
\][/tex]
The goal is to find the vector [tex]\(\mathbf{x}\)[/tex] that satisfies this equation.
Using matrix inversion and multiplication, we find:
[tex]\[ \mathbf{x} = A^{-1} \mathbf{b} \][/tex]
Solving this will give us the values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Thus, the ordered pair [tex]\((x, y)\)[/tex] that satisfies the system of equations is:
[tex]\[
(x, y) = (3.0, 2.0)
\][/tex]
So, the solution is the ordered pair [tex]\((3.0, 2.0)\)[/tex].
