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Solve the following system of equations using an inverse matrix. You must also indicate the inverse matrix, A-1, that was used to solve the system. You may optionally write the inverse matrix with a scalar coefficient.

Solve the following system of equations using an inverse matrix You must also indicate the inverse matrix A1 that was used to solve the system You may optionall class=

Respuesta :

[tex]\begin{cases}5x-3y={8} \\ 7x-5y={4}\end{cases}[/tex]

start multiplying the first equation by 7 and the second by 5

[tex]\begin{gathered} 7\ast(5x-3y=8) \\ 5\ast(7x-5y=4) \\ then, \\ 35x-21y=56 \\ 35x-25y=20 \end{gathered}[/tex]

then, subtract both of the equations,

[tex]\begin{gathered} 35x-21y-(35x-25y)=56-20 \\ -21y+25y=36 \\ 4y=36 \end{gathered}[/tex]

solve for y

[tex]\begin{gathered} y=\frac{36}{4} \\ y=9 \end{gathered}[/tex]

substitute in the first equation,

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