Solve the simultaneous equations: 4x+3y=5 and x-y=3, to find the values of x and y.

First of all, we need to get the equations in a form so that either x or y can be eliminated.

In this case, I have a positive amount of y, and a negative amount of y, meaning that I can add the two equations together, once I have made my amounts of y equal. To do this, I will multiply the second equation by 3 to give: 3x-3y=9. When I add this to the first equation I get (4x+3x)+(3y-3y)=(5+9), as when I add a negative number, this is the same as subtraction. So I get 7x=14, which dividing both sides by 7 gives x=2.

However, the question also requires me to find a value for y, so I substite my new value of x into the second equation of the question, so 2-y=3, therefore y=2-3, which gives y=-1.

Therefore we have x=2 and y=-1 as our answer.