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How do you solve by substitution: $y = - x + 5$ $y=-x+5$ and $3 x - y = - 1$ $3x-y=-1$ ?

1 Answer

Oct 1, 2015

Substitute the expression given for $y$ $y$ by the first equation for $y$ $y$ in the second equation and simplify to get
#(x,y)=(1,4)

Explanation:

[1] $XXX y = - x + 5$ $color(white)("XXX")y=-x+5$
[2] $XXX 3 x - y = - 1$ $color(white)("XXX")3x-y=-1$

Substituting $(- x + 5)$ $(-x+5)$ from [1] into $[2]$ $[2]$ in place of $y$ $y$
[3] $XXX 3 x - (- x + 5) = - 1$ $color(white)("XXX")3x-(-x+5) = -1$

Simplifying
[4] $XXX 4 x - 5 = - 1$ $color(white)("XXX")4x-5 = -1$

[5] $XXX 4 x = 4$ $color(white)("XXX")4x = 4$

[6] $XXX x = 1$ $color(white)("XXX")x=1$

Substituting $1$ $1$ for $x$ $x$
[7] $XXX y = - 1 + 5$ $color(white)("XXX")y =- 1+5$

[8] $XXX y = 4$ $color(white)("XXX")y=4$

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