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How do you solve $3 x + y = 2$ $3x + y = 2$ and $4 x + y = 20$ $4x + y = 20$ using substitution?

1 Answer

Mar 14, 2018

$(x, y) = (18, - 52)$ $(x,y)=(18,-52)$

Explanation:

Given
[1] $XXX 3 x + y = 2$ $color(white)("XXX")3x+y=2$
[2] $XXX 4 x + y = 20$ $color(white)("XXX")4x+y=20$

We can re-arrange [1] into the form:
[3] $XXX y = 2 - 3 x$ $color(white)("XXX")y=2-3x$

Then we can substitute (as requested) $(2 - 3 x)$ $(2-3x)$ for $y$ $y$ in [2]
[4] $XXX 4 x + (2 - 3 x) = 20$ $color(white)("XXX")4x+(2-3x)=20$

Simplifying [4]
[5] $XXX x + 2 = 20$ $color(white)("XXX")x+2=20$

The subtracting $2$ $2$ from both sides of [5]
[6] $XXX x = 18$ $color(white)("XXX")x=18$

Based on [6], we can now substitute $18$ $18$ for $x$ $x$ in [1]
[7] $XXX 3 \cdot 18 + y = 2$ $color(white)("XXX")3 * 18 +y=2$

With some simplification
[8] $XXX 54 + y = 2$ $color(white)("XXX")54+y=2$

[9] $XXX y = - 52$ $color(white)("XXX")y=-52$

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