3x+5y=7 and 9x+11y=13. Solve to find the values of x and y that satisfy both equations.

As there are two unknowns we have to eliminate either the x or the y in order to be able to solve. You can see that in the first equation the x value is a multiple of the x value in the second equation. Therefore if we multiple the first equation by 3 we get the same amount of x. This gives us a new equation of 9x+15y=21. We can now subtract the second equation from the first so that we get 0x+4y=8 meaning y=2. Now that we know what y equals we can substitute it into either one of the equations we were given. For example 3x+5(2)=7 so 3x+10=7. Then we just solve this how we would do for a basic algebraic equation so 3x=-3 so x=-1. Therefore x=-1 and y=2. You can check these values are correct by substituting them into the second equation and they should give the answer.