How do you solve $y = | x |$ $y=|x|$ and $y = \frac{1}{2} x + 4$ $y=1/2x+4$ using substitution?

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How do you solve $y = | x |$ $y=|x|$ and $y = \frac{1}{2} x + 4$ $y=1/2x+4$ using substitution?

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Answer 1 · 2018-02-12T01:09:16

$(x, y) = (8, 8)$ $(x,y)=(8,8)$ or $(x, y) = (- \frac{8}{3}, \frac{8}{3})$ $(x,y)=(-8/3,8/3)$

Explanation:

Given
[1] $XXX y = | x |$ $color(white)("XXX")y=abs(x)$
[2] $XXX y = \frac{1}{2} x + 4$ $color(white)("XXX")y=1/2x+4$

Substituting $| x |$ $abs(x)$ for $y$ $y$ (based on [1])
in [2], we get:
[3] $XXX | x | = \frac{1}{2} x + 4$ $color(white)("XXX")abs(x)=1/2x+4$

which implies:
${: ("either ",[4]color(white)("xx")-x=1/2x+4," or ",[8]color(white)("xx")x=1/2x+4), (,rarr[5]color(white)("xx")-3/2x=4,,rarr[9]color(white)("xx")1/2x=4), (,rarr[6]color(white)("xx")x=-8/3,,rarr[10]color(white)("xx")x=8), ("then based on [1]",,,), (,rarr[7]color(white)("xx")y=8," or ",rarr[11]color(white)("xx")y=8/3) :}$

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How do you solve $y = | x |$ $y=|x|$ and $y = \frac{1}{2} x + 4$ $y=1/2x+4$ using substitution?

1 Answer

Explanation:

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How do you solve $y = | x |$ $y=|x|$ and $y = \frac{1}{2} x + 4$ $y=1/2x+4$ using substitution?