Solve the simultaneous equations to find the values of x and y: 3x + 5y = -4 and 10x - 4y = -34

Firstly we need to remove one of the variables. We can use the fact that y has different signs to do this.
3x + 5y = -4 multiplied by 4 gives: 12x + 20y = -16
10x - 4y = -34 multiplied by 5 gives: 50x - 20y = -170
If we add these together we get: 62x = -186
If we divide both sides by 62, this gives: x = -3
Substituting this back into the first equation gives: -9 + 5y = -4
Adding 9 to both sides: 5y = 5
Therefore, dividing both sides by 5 gives: y = 1
This can be checked by substituting these values into the second equation: -30 - 4 = -34
Therefore, as both sides equal -34, we know these values are correct.