solve the simultaneous equation: 8x+2y=46; 7x+3y=47

To solve this problem, we want to make either the x or the y values either equation the same.To work out whether to change the x or the y values, work out the lowest common multiple for each.For x, the values are 7 and 8 so the lowest common multiple is 56For y, the values are 2 and 3 so the lowest common multiple is 6 - this is lower hence we will change the y valuesto get 6y in each equation, multiply the first by 3 (as 2y x 3 = 6y) and the second by 2 (as 3y x 2 = 6y)This will give:24x+6y=13814x+6y=94minusing the bottom equation from the top one will eliminate the y values and give:10x = 44therefore dividing by 10:x=4.4