Solve the following simultaneous equations: 3x + y = 11 2x + y = 8

Start off by determining which unknowns have the same coefficient-      In this case it would be y as the coefficient of y is 1 in both equationsThen make both equations equal to y-      So 3x+y= 11 would become y= 11-3x2x+y= 8 would become y=8-2xNow that both equations are equal to y, this means the must be equal to each otherso we can re-write the equations like this: -      11-3x=8-2xTo solve for x we need to get all the x's on one side, and all the numbers on the other side-      Because they are equal, what we do to one side we must do to the other-      If we add 3x to each side we will get: 11=8+x-      Then to get all the numbers on the opposite side, we'd need to -8 from both sides, this would give us: 3=xSo now we know x=3, to find y we can substitute x into either of the very first equations-      If we take 2x+y=8 and substitute in x=3: 2(3)+y=8 which is the same as 6+y=8-      Which would mean, y=2So we have our answer, x=3 and y=2-      you can check this by substituting x and y into the other first equation (3x + y = 11)-      3(3) + 2= 9+2 =11