Answer :
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].
[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].
