# How do you solve 2x + y = 7 and y - x = 1  using substitution?

Mar 8, 2018

$\therefore$ color(darkred)(x=2 and y=3

#### Explanation:

$2 x + y = 7$

$y = 7 - 2 x$

Given that,

$y - x = 1$

Substituting $y = 7 - 2 x$

$7 - 2 x - x = 1$

$7 - 3 x = 1$

$- 3 x = 1 - 7$

$- 3 x = - 6$

$x = \frac{- 6}{-} 3$

color(magenta)(x=2

$y = 7 - 2 x$

$y = 7 - 2 \times 2$

$y = 7 - 4$

color(magenta)(y=3

$\therefore$ color(darkred)(x=2 and y=3

~Hope this helps! :)

Mar 8, 2018

$y = 3 , x = 2$

#### Explanation:

$2 x + y = 7 - - - - - - \left(1\right)$
$- x + y = 1 - - - - - - - - \left(2\right)$

$\left(1\right) - \left(2\right)$

$3 x = 6$

$x = \frac{6}{3}$

$x = 2$

substitute $x = 2$ in $\left(2\right)$

$\therefore - \left(2\right) + y = 1$

$\therefore y = 1 + 2$

$\therefore y = 3$
~~~~~~~~~~~
check:-

substitute $y = 3 \mathmr{and} x = 2$ in (1)

$\therefore 2 \left(2\right) + \left(3\right) = 7$

$\therefore 4 + 3 = 7$