# How do you solve the following linear system: 3x - 6y = 9 , y = 1/2x - 3/2 ?

Feb 7, 2016

Solve by substitution:

$3 x - 6 y = 9 , y = \frac{1}{2} x - \frac{3}{2}$

In the second equation the value of $y$ can be substituted to the first equation:

$\rightarrow 3 x - 6 \left(\frac{1}{2} x - \frac{3}{2}\right) = 9$

Use distributive property ($a \left(b + c\right) = a b + a c$):

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

$\rightarrow 3 x - 3 x + 9 = 9$

$\rightarrow 9 = 9$

So,if you see a equation ending like this,they mean that the value is possible for all real numbers.The value of $x$ is all the real numbers in mathematics.

Now we know that $x$ corresponds to all real numbers.So, $y$ is as same as the second equation:

$\implies y = \frac{1}{2} x - \frac{3}{2}$