Solve the following simultaneous equations for x and y. 2x+5y=9 and 4x-3y=7

Here the best method to use will be elimination since using a substitution for x or y may produce some nasty fractions. The first thing to look for is that the 2x and 4x are nice multiples of each other. As a result we should try to eliminate the x terms. So if we multiply equation 1 by 2 we reach 4x+10y=18. (Call this equation 3). Now we subtract equation 2 from equation 3. This gives 13y=11. So y=11/13. Now we substitute this y value into either equation, lets use 1. 2x+(511/13)=9 so 2x=62/13 and therefore x=31/13. We can test our solutions to be sure in equation 2 and see that (431/13)-(3*11/13)=7