# x+y=10" " and x-y=2 What is x?

Apr 25, 2018

$x = 6 , y = 4$

#### Explanation:

$| \left(x + y = 10\right) , \left(x - y = 2\right) |$
$x + x + y - y = 10 + 2$
2x=12|:2
$x = 6$
Sub the result into any of the two equations for $x$
$6 + y = 10 | - 6$
$y = 4$

Apr 25, 2018

$x = 6$
$y = 4$

#### Explanation:

Given
$x + y = 10$
x-y=  2
Solve for $x$

This is a Simultaneous Equations problem.

Add the equations to let $y$ drop out as zero

$\textcolor{w h i t e}{m}$$x + y = 10$
$\textcolor{w h i t e}{m}$x-y=   2
$\textcolor{w h i t e}{}$―――――――
2x   color(lightgray) (+ 0) =  12
$\textcolor{w h i t e}{n}$xcolor(white)(mnn)=   6 $\leftarrow$ answer

If $x$ equals $6$, then $y$ must equal $4$

$\textcolor{w h i t e}{m m m m m m}$―――――――

Check

Sub in the values in the place of the letters to verify that the equations are still correct.

$\textcolor{w h i t e}{m}$$x + y = 10$
$\textcolor{w h i t e}{m}$$6 + 4 = 10$  ✓

$\textcolor{w h i t e}{m}$$x - y = 2$
$\textcolor{w h i t e}{m}$$6 - 4 = 2$  ✓

$C h e c k$