How do solve the following linear system?: $-10x+7y=-2 , x-y=11$ ?

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Answer 1 · 2017-02-07T13:14:13

See the entire solution process below:

Step 1) Solve for $x$ in the second equation:

$x - y + color(red)(y) = 11 + color(red)(y)$

$x - 0 = 11 + y$

$x = 11 + y$

Step 2) Substitute $11 + y$ for $x$ in the first equation and solve for $y$ :

$-10x + 7y = -2$ becomes:

$-10(11 + y) + 7y = -2$

$-110 - 10y + 7y = -2$

$-110 - 3y = -2$

$-110 + color(red)(110) - 3y = -2 + color(red)(110)$

$0 - 3y = 108$

$-3y = 108$

$(-3y)/color(red)(-3) = 108/color(red)(-3)$

$(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = -36$

$y = -36$

Step 3) Substitute $-36$ for $y$ in the solution to the second equation at the end of Step 1 and solve for $x$ :

$x = 11 + y$ becomes:

$x = 11 - 36$

$x = -25$

The solution is: $x = -25$ and $y = -36$

How do solve the following linear system?: -10x+7y=-2 , x-y=11 -10x+7y=-2 , x-y=11 ?