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

Aug 2, 2018

#### Explanation:

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

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

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

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

or $x \left(2 x - 5\right) + 2 \left(2 x - 5\right) = 0$

or $\left(x + 2\right) \left(2 x - 5\right) = 0$

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

or $2 x - 5 = 0$ i.e. $x = \frac{5}{2} = 2.5$

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

$y = 4$ or $y = 6.25$