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How do you solve $9x - y = 317$ and $10x - 11y = 550$ using substitution?

1 Answer

Jun 9, 2016

$(x,y)=color(green)(""(33,-20))$
(see below for solution by substitution)

Explanation:

Given
[1] $color(white)("XXX")9x-y=317$
[2] $color(white)("XXX")10x-11y=550$

We can re-arrange [1] as
[3] $color(white)("XXX")y=9x-317$

Using [3] we can substitute $9x-317$ for $y$ in [2]
[4] $color(white)("XXX")10x-11(9x-317)=550$

[5] $color(white)("XXX")10x-99x=550-3487$

[6] $color(white)("XXX")89x=2937$

[7] $color(white)("XXX")x=33$

Using [7] we can substitute $33$ for $x$ in [1]
[8] $color(white)("XXX")9(33)-y=317$

[9] $color(white)("XXX")297-y=317$

[10] $color(white)("XXX")y=-20$

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