Solve the following simultaneous equations: 2x-3y=16 x+2y=-6

First, label the two equations as follows:2x-3y=16 --> [1]x+2y=-6 --> [2]To obtain the same x value for both equations, [2]2: 2x+4y=-12 --> [3]Then, to eliminate the x values from both equations, [1]-[3]: -7y=28, therefore y=-4To obtain the x value, substitute the calculated y value into either equation (could do the other to double check) as follows:Into equation [1]: 2x-3(-4)=16, therefore 2x=4, so x=2 (Check with equation [2]: x+2*(-4)=-6, therefore x=2)Alternative method would be to match the two y values to make it 6y in both equations, but given that both equations need to be altered for this, it is much more inefficient and therefore the described method is much more desirable. Answer: x=2, y=-4