How do I solve the simultaneous equations 5x+2y=11 and 4x-3y=18?

Simultaneous equations have two or more unknown values, in this case there are two: x and y. To solve them, first we need to get one unknown by itself. In order to do this we need the coefficient of either x or y to be the same number in both equations. If we multiply the first equation by 3 we get: 15x+6y=33. If we multiply the second equation by 2 we get: 8x-6y=36. The coefficient of y is 6 in both equations so now we can eliminate the y values. As we have a positive and a negative value, adding the two equations together will cancel out the y values: 23x=69. If both values were positive, we would need to subtract one equation from the other instead. 23x=69 can be easily solved to give x=3. Then we just replace the x in one of the original equations to find y: 5(3)+2y =11 --> 2y = -4 --> y=-2. You can then check your answers by substituting back into the other equation.