# How do you solve this system of equations by substitution:  - x+y = 40 and y = 9x?

Dec 10, 2017

$x = 5 \mathmr{and} y = 45$

#### Explanation:

$- x + y = 40$ ----- let this be equation (1)and
$y = 9 x$ ------be equation (2)

Substitute value of $y$ from equation(2) in equation(1):

(1) $\implies - x + \left(9 x\right) = 40$

$\implies 8 x = 40$

$\implies x = \frac{40}{8} = 5$

Now substitute this value of $x$ in equation(2) :

$\implies y = 9 x = 9 \times 5 = 45$

$\therefore x = 5 \mathmr{and} y = 45$

Dec 10, 2017

x,y)to(5,45)

#### Explanation:

$- x + y = 40 \to \left(1\right)$

$y = 9 x \to \left(2\right)$

$\textcolor{b l u e}{\text{substitute "y=9x" into equation }} \left(1\right)$

$- x + 9 x = 40$

$\Rightarrow 8 x = 40$

$\text{divide both sides by 8}$

$\frac{\cancel{8} x}{\cancel{8}} = \frac{40}{8}$

$\Rightarrow x = 5$

$\text{substitute this value into equation } \left(2\right)$

$y = 9 \times 5 = 45$

$\Rightarrow \text{point of intersection } = \left(5 , 45\right)$