Solve this set of simultaneous equations. 1. 4x+2y=12 2. 2x+3y=10

To solve simultaneous equations we need to make either the y coefficients or the x coefficients equal so that we can cancel them out. For this set of equations we are going to make the x coefficients the same. To make them the same we need to find a common factor. In this example the common factor of 4 and 2 is 4. We need to multiply our equations to make 4 the coefficient of x for both. Therefore, we need to multiply equation 1 by 1 and equation 2 by 2. This gives us the equations 1. 4x+2y=12 and 2. 4x+6y=20. In order to cancel out the x's we need to subtract equation 1 from equation 2. This gives 4y=8. We are now able to work out the value of y as only have one unknown. To find y we divide both sides by 4 so y=2.
Now that we know the value of y we can substitute it into one of the original equations to find the value of x. We know y=2 so if we substitute this into equation 1 this gives us 4x+4=12. We now only have one unknown in this equation so can rearrange it to find x. Subtract 4 from both sides to get 4x=8. Finally divide both sides by 4 to give x=2. The final answer is y=2, x=2.