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How do you find the solution set for x-y=11, 3x+10y=-6?

1 Answer

Aug 6, 2015

$(x, y) = (8, - 3)$ $(x,y) = (8,-3)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $x - y = 11$ $x-y=11$
[2] $XXXX$ $color(white)("XXXX")$ $3 x + 10 y = - 6$ $3x+10y = -6$

Multiply [1] by 3
[3] $XXXX$ $color(white)("XXXX")$ $3 x - 3 y = 33$ $3x-3y = 33$

Subtract [3] from [2]
[4] $XXXX$ $color(white)("XXXX")$ $13 y = - 39$ $13y = -39$

Divide [4] by 13
[5] $XXXX$ $color(white)("XXXX")$ $y = - 3$ $y=-3$

Substitute $(- 3)$ $(-3)$ for $y$ $y$ in [1]
[6] $XXXX$ $color(white)("XXXX")$ x- (-3) = 11#

Simplify
[7] $XXXX$ $color(white)("XXXX")$ $x + 3 = 11$ $x+3 = 11$

Subtract 3 from both sides of [7]
[8] $XXXX$ $color(white)("XXXX")$ $x = 8$ $x=8$

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