Solve for x and y: 2x +5y + 5= 0 , 2y + 31= 5x

For a question like this you should aim to eliminate either x OR y from one equation in order to deduce the value of the other. 1) 2x +5y + 5= 0 , 2) 2y + 31= 5x
Rearrange equation 2) so that 2y +31= 5x --> 5x -2y -31 = 0
Now multiply equation 1) by 2 and equation 2) by 5 (this will allow you to cancel the y in the next step)1) 2x+ 5y+5 (multiply by 2) --> 4x +10y +10 , 2) 5x -2y -31=0 (multiply by 5)--> 25x -10y -155 =0
We will now add these 2 equations together. This will allow us to find the value of x as y will be cancelled out (as equation 2 is -y)(4x +10y +10) + (25x -10y -155) --> 29x -145 =0 From this we can work out the value of x --> 29x = 145 therefore x= 5
Now to work out y, just substitute the value of x into either equation 1 or 2. I have shown you below with both for your understanding. x=5 subbed into equation 1) --> (2x5) +5y +5 =0 --> 15 +5y =0 --> 5y = -15 --> y= -3x=5 subbed into equation 2) --> 2y +31 = (5x5) --> 2y = (25- 31) --> 2y = -6 --> y=-3