# How do you solve y = 3 - 1/2 x, 3x + 4y = 1?

Jun 26, 2016

$x = - 11 , y = 8 \frac{1}{2}$

#### Explanation:

Substitution seems quite a good method to choose, because $y$ is given as the subject in one of the equations.

$y = \left(3 - \frac{1}{2} x\right)$ can be substituted into $3 x + 4 y = 1$

ie. Use$\left(3 - \frac{1}{2} x\right)$ in the place of $y$ in the second equation:

$3 x + 4 \left(3 - \frac{1}{2} x\right) = 1 \text{ }$ now there are only x-terms.

$3 x + 12 - 2 x = 1$

$x = - 11$

Now that we have the value for $x$, use it to find the value of $y$.

$y = \left(3 - \frac{1}{2} x\right) \Rightarrow = 3 - \frac{1}{2} \left(- 11\right)$

$y = 3 + 5 \frac{1}{2} \Rightarrow y = 8 \frac{1}{2}$