How do solve the following linear system?: $-x+5y=-13 , -4x-15y=-1$ ?

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Answer 1 · 2015-11-25T01:50:26

$x=(-40)/7$
$y=(-51)/35$

Given -

$-x+5y=-13$ ----------------(1)
$-4x-15y=-1$ --------------(2)

Solve equation (1) for $x$

$-x=-13-5y$
$x=13+5y$

Substitute $x=13+5y$ in equation (2)

$-4(13+5y)-15y=-1$

$-52-20y-15y=-1$
$-52-35y=-1$
$-35y=-1+52=51$
$-35y=51$
$y=(51)/(-35)=(-51)/35$
$y=(-51)/35$

Substitute $y=(-51)/35$ in equation (1)

$-x+5(-51/35)=-13$
$-x-255/35=-13$
$-x-51/7=-13$
$-x=-13+51/7=(-91+51)/7=(-40)/7$
$x=(-40)/7$

How do solve the following linear system?: -x+5y=-13 , -4x-15y=-1 -x+5y=-13 , -4x-15y=-1 ?