# Solve the linear system of equations.−5x −2y= 12x −11y=−83(x, y) =

Solve the linear system of equations.
$-5x-2y=1$
$2x-11y=-83$
$\left(x,y\right)=$

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Brighton

consider the given equations
$-5x-2y=1$----(1)
$2x-11y=-83$---(2)
Multiply in equation (1)by(2) and multiply in equation (2)by 5
$2\left(-5x-2y\right)=1$---(2)
$-10x-4y=2$---(3)
and
$5\left(2x-11y\right)=-83\left(5\right)$
$10x-55y=-415\left(4\right)$
$-10x-4y+10x-55y=2-415$
$-59y=-413$
$y=\frac{413}{59}$
$=7$
put value of $y=7$ in equation(1)
$-5x-2\left(7\right)=1$
$-5x-14=1$
$-5x=1+14|$
$-5x=15$
$x=-3$