How do you solve $y=x^2$ and $y= 0.5x + 5$ using substitution?

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Answer 1 · 2018-08-02T14:59:13

Please see below.

Just substitute value of $y$ from equation $y=0.5x+5$ in $y=x^2$

and we get $0.5x+5=x^2$ and multiplying by $2$ , we get

$x+10=2x^2$ or $2x^2-x-10=0$

i.e. $2x^2-5x+4x-10=0$

or $x(2x-5)+2(2x-5)=0$

or $(x+2)(2x-5)=0$

i.e. either $x+2=0$ i.e. $x=-2$

or $2x-5=0$ i.e. $x=5/2=2.5$

Putting these values of $x$ in $y=0.5x+5$ , we get

$y=4$ or $y=6.25$

How do you solve y=x^2 y=x^2 and y= 0.5x + 5y= 0.5x + 5 using substitution?