To solve for this, we need to figure out the value for each variable. Both of these values must work for each of the variables in both equations.
Although I've already solved for the variables in my head, I'll just use them as the example for this anyways.
6x + 7y = 59 Let's plug in "4" for x, and "5" for y. 6(4) + 7(5) 24 + 35 59. < -- this value works, but let's continue with our second equation just to be sure.
4x + 5y = 41 Once again, let's plug in "4" for x, and "5" for y. 4(4) + 5(5) 16 + 25 41. < -- this value also works, so we now have our answers.
The value for 'x' is "4", and the value for 'y' is "5".