How do you solve 6x-y=-5 and 4x-2y=6?

Oct 8, 2015

$x = \frac{1}{2}$

$y = - 2$

Explanation:

We have 2 equations and 2 unknowns so they are simultaneous.

$6 x - y = 5 \text{ } \textcolor{red}{\left(1\right)}$

$4 x - 2 y = 6 \text{ } \textcolor{red}{\left(2\right)}$

From $\textcolor{red}{\left(1\right)} :$

$y = \left(6 x - 5\right)$

We can substitute this expression for $y$ into $\textcolor{red}{\left(2\right)} \Rightarrow$

$4 x - 2 \left(6 x - 5\right) = 6$

$4 x - 12 x + 10 = 6$

$- 8 x = 6 - 10$

$- 8 x = - 4$

$x = \frac{- 4}{-} 8 = \frac{1}{2}$

We can now substitute this value of $x$ into $\textcolor{red}{\left(1\right)} \Rightarrow$

$6 \times \frac{1}{2} - y = 5$

$3 - y = 5$

$y = 3 - 5 = - 2$