# How do you find the ordered pair that is a solution to the system of equations x + y = 10 and x - y = 8?

Jul 17, 2018

$x = 9 , y = 1$

#### Explanation:

$2 x = 18$
so $x = 9$

and we get for $y$

$9 + y = 10$
$y = 1$

Jul 17, 2018

$\left(x , y\right) \to \left(9 , 1\right)$

#### Explanation:

$x + y = 10 \to \left(1\right)$

$x - y = 8 \to \left(2\right)$

$\text{adding the 2 equations term by term eliminates } y$

x+x)+(y-y)=(10+8)

$2 x = 18 \Rightarrow x = \frac{18}{2} = 9$

$\text{substitute "x=9" into equation } \left(1\right)$

$9 + y = 10 \Rightarrow y = 10 - 9 = 1$

$\text{the point of intersection } = \left(9 , 1\right)$
graph{(y+x-10)(y-x+8)((x-9)^2+(y-1)^2-0.04)=0 [-20, 20, -10, 10]}