How do you solve the following system?:  x + 3-2y=7 , y=2x+9

Mar 9, 2016

$\left(x , y\right) = \left(- \frac{22}{3} , - \frac{17}{3}\right)$

Explanation:

1)x+3-2y=7

2)y=2x+9

Substitute the value of $y$ to the first equation

$\rightarrow x + 3 - 2 \left(2 x + 9\right) = 7$

$\rightarrow x + 3 - 4 x - 8 = 7$

$\rightarrow x + 3 - 4 x = 7 + 18$

$\rightarrow x + 3 - 4 x = 25$

$\rightarrow x - 4 x = 25 - 3$

$\rightarrow x - 4 x = 22$

$\rightarrow - 3 x = 22$

$\Rightarrow x = - \frac{22}{3}$

Now,Substitute the value of $x$ to the second equation

$\rightarrow y = 2 \left(- \frac{22}{3}\right) + 9$

$\rightarrow y = - \frac{44}{3} + 9$

$\Rightarrow y = - \frac{17}{3}$