# How do you solve the system x= 3y-1 and x+2y=9?

Apr 16, 2018

Arrange the equations. You get $x = 5$ and $y = 2$

#### Explanation:

$x - 3 y = - 1$
$- x - 2 y = - 9$

(after multiplying the 2nd equation by -1#

$- 5 y = - 10$

$y = 2$

Put this value in the 1st original equation:
$x - \left(3 \times 2\right) = - 1$
$x - 6 = - 1$
$x = - 1 + 6$
$x = 5$

Apr 16, 2018

$\left(x , y\right) \to \left(5 , 2\right)$

#### Explanation:

$x = 3 y - 1 \to \left(1\right)$

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

$\text{rearrange equation "(2)" to give x in terms of y}$

$\Rightarrow x = 9 - 2 y \to \left(3\right)$

$\text{since "(1)" and "(3)" both give x in terms of y we}$
$\text{can equate the right sides}$

$\Rightarrow 3 y - 1 = 9 - 2 y$

$\text{add 2y to both sides}$

$3 y + 2 y - 1 = 9 \cancel{- 2 y} \cancel{+ 2 y}$

$\Rightarrow 5 y - 1 = 9$

$\text{add 1 to both sides}$

$\Rightarrow 5 y = 10 \Rightarrow y = 2$

$\text{substitute "y=2" in either "(1)" or } \left(3\right)$

$\left(1\right) \to x = 6 - 1 = 5$

$\text{solution is } \left(x , y\right) \to \left(5 , 2\right)$