Question

How do you solve the system of equations `-8x + 3y = 7` and `13x - 3y = - 17`?

Answer 1

See explanation.

Explanation:

The starting system can be written as:

`{(-8x+3y=7),(13x-3y=-17) :}`

We can see that the coefficients of `y` are opposite numbers, so if we add both sides of the equations we get rid of one variable:

`5x=-10 => x=-2`

Now if we substitute the calculated value of `x` to any of the equations we can calculate the remaining variable `y`:

`-8*(-2)+3y=7`

`16-3y=7`

`-3y=-9 => y=-3`

Finally we can write that the solution is:

`{(x=-2),(y=-3) :}`