# How do you solve 3x + y = -26 and 2x - y = -19?

Sep 5, 2015

$x = - 9$ and $y = 1$

#### Explanation:

Using the method of simultaneous equations, you take the first equation and write $y$ in terms of $x$ to get

$y = - 3 x - 26$

Then you substitute this into the second equation, ie. wherever you see a $y$ in the second equation, you replace it with $\left(- 3 x - 26\right)$. This yields

$2 x - \left(- 3 x - 26\right) = - 19$

This then leaves an equation with only one unknown, $x$, so we may solve or $x$ to obtain

$5 x + 26 = - 19$

Therefore $x = - 9$.

Then substitute back to get the value or $y$ as

$- 3 \cdot \left(- 9\right) - 26 = 1$

An alternative method would be to use linear matrix algebra, in which a separate 3 methods exist :

• Gauss-Jordan elimination
• Inverse matrix method
• Kramer's Rule

Please let me know if you require me to resolve the problem using any of these 3 methods and I will do so for you, otherwise the simultaneous equation method shown above should suffice or a $2 \times 2$ linear system. The matrix methods are more time efficient for higher order systems like $3 \times 3$ and higher.