Question

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

Answer 1

`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=-3x-26`

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

`2x-(-3x-26)=-19`

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

`5x+26=-19`

Therefore `x = - 9`.

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

`-3 * (-9) -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 xx 2` linear system. The matrix methods are more time efficient for higher order systems like `3 xx 3` and higher.