Solve 2x+y=6, 3x+2y=3 for x and y.

Give each equation a label:(1) 2x+y=6(2) 3x+2y=3Multiply one equation to make the number of x's or y's the same in each equation. 2 X (1) : 2(2x+y=6) 4x+2y=12 (2) 3x+2y=3There are now 2y's in each equation therefore will cancel each other out in next sum.Either add or subtract one equation from other depending of signs of equal letters (in this case y), if signs are the same, (eg. +2y and +2y) then subtract ( eqn (1) - eqn (2) ). If the signs are different (eg. +2y - 2y) then add ( eqn (1) + eqn (2) ). In this case the signs are the same therefore we will subtract. 2 X (1): 4x+2y=12 -(2) - 3x+2y=3, x =9Substitute x=9 into equation (1): 2x+y=6 2(9)+y=6 18+y=6 y=6-18 y=-12Substitute x and y values into equation (2) to check answer is correct:3x+2y=3LHS= 3(9)+2(-12) 27-24 3RHS=3Therefore LHS=RHS, so we know that x=9 and y=-12.