Question

How do you solve the following system?: `13x +17y =11, -6x +5y = -27`

Answer 1

Express y in terms of x and insert the expression in the other equation.

Explanation:

Substitution means expressing one variable in terms of another. So, you'll need to remake the expression in such a way that x (or y, doesn't matter) will be alone on one side of the equation.

Let's pick the second one for this, since it seems easier:
`-6x + 5y = -27`
`-6x = -5y - 27`
`x = 5/6y + 4.5`

Then, insert the last expression in the other equation:
`13x+17y=11`
`13(5/6y+4.5)+17y=11`
`65/6y+58.5+17y=11`
`65/6y+102/6y=-58.5+11`
`167/6y = -47.5`
`167/6y = -285/6`
`167y = -285`
`y = -285/167` which is around -1.7066.

Then, replace the found y in the equation with isolated x to find x:
`x=5/6*(-285/167) + 4.5`
`x=3.0778`

And finally, the answer is:
`x = 3.0778`
`y=-1.7066`