# What is y and x when y= 2x-11 and y= x- 8 ?

Apr 5, 2017

x = + 3 y = -5

#### Explanation:

One way to solve the problem is to subtract the two equations from each other.

 y = 2x - 11 - (y = x - 8 )

$y - y = 0$
$2 x - x = x$
$- 11 - \left(- 8\right) = - 3$

so $y = 2 x - 11 - \left(y = x - 8\right) = \left\{0 = x - 3\right\}$

Solving for $0 = x - 3$ add 3 to both sides giving

$0 + 3 = x - 3 + 3$ so

$+ 3 = x$

now put the value of +3 into either equation and solve for y

$y = + 3 - 8$

$y = - 5$

To check put these values into the second equation

$- 5 = 2 \left(+ 3\right) - 11$

$- 5 = + 6 - 11$

 -5 = -5 check

x = +3 y = -5

Apr 5, 2017

color(red)(y=-5,x=3

#### Explanation:

$y = 2 x - 11$ ------(1)

$y = x - 8$ ---------(2)

$\left(2\right) \times 2$

$2 y = 2 x - 16$ ------(3)

$\left(1\right) - \left(3\right)$

$- y = 5$

color(red)(y=-5

substitute color(red)(y=-5 in (2)

$\textcolor{red}{- 5} = x - 8$

$x - 8 = - 5$

$x = - 5 + 8$

color(red)(x=3

substitute color(red)(y=-5,x=3# in (1)

$\textcolor{red}{- 5} = 2 \left(\textcolor{red}{3}\right) - 11$

$- 5 = 6 - 11$

$- 5 = - 5$