Solve the simultaneous equations equation 1: 2x+3y=4 and equation 2: 5x+6y=7

This question can be solved by many methods but the elimination method is the fastest one in this case.  The unknown that will be eliminated is y. Equation 1 is multiplied by 2 to give 4x+6y=8. Since I have chosen to eliminate y, I will now subtract equation 1 from equation 2 as this will leave us with the x as the only unknown. So:  5x+6y-4x-6y=7-8 This gives x=-1 which can be substituted in either of equation 1 or 2 to solve for y. If we substitute in equation 1 we get 2*(-1)+3y=4 so y=2. We can check that the answer is correct by substituting x and y in either equation to confirm that it's equal to the right hand side of the equation.  So for equation 2: 5*(-1)+6*2=7 which is what was expected so the answer is correct.