Solve the following simultaneous equations, 1) 3x + 3y = 9 and 2) 4x + 2y = 13.

Solving the above question means to find a value of x and y that satisfies both equations. To solve this we first have to look at the x terms and y terms and decide which terms are the easiest to cancel out. If we are able to get cancel out, for example, the x terms, then we are just left with the y terms and the equations can be solved for y and then x can be found. This same method can be used if the y terms are cancelled out first. In our case, let's choose the y terms to cancel out. To do this, we have to find the lowest common multiple of 2 and 3, which is 6. So, multiply equation 1) by 2, this gives 6x + 6y = 18. Next, multiply equation 2) by 3, this gives 4x + 6y = 26.Now, we can see that 6y exists in both equations. To cancel out the y terms in both equations we have to substract one of the equations from the other. In our case, we can subtract new equation 2) from new equation 1), and the 6y term in both equations will cancel each other out: 6x + 6y = 18, -12x +- 6y =-39, -6x = -21 (these equations would be written in a column)Therefore, solving the above equation for x is simply by dividing both sides by -6 and we obtain x = 3.5. To find y, we can just subsitute x = 3.5 into equation 1) (or equation 2) ), 3(3.5) + 3y = 9, which gives y = -0.5. To check that these are the correct values for x and y, substitute them back into equation 2) to check (or equation 1) if equation 2) was used to find y), e.g. 4(3.5) + 2(-0.5) = 13.