Question

Solve for X and Y using elimination method

X/3 + Y/4 = 11

5X/6 - Y/3 + 7 = 8

Answer 1

Solution by elimination:

4x + 3y = 132
5x - 2y = - 42

let's multiply both sides of the second equation by 3/2 in order to change the coefficient of y in the second equation into - 3:

4x + 3y = 132
(3/2)(5x - 2y) = - 42(3/2)

4x + 3y = 132
(15/2)x - 3y = - 21(3)

4x + 3y = 132
(15/2)x - 3y = - 63

let's now add the first and the second equation together:

4x............ + 3y = 132
(15/2)x..... - 3y = - 63
----------------------- --------
[4+(15/2)]x + 0 = 132 - 63

[(8 + 15)/2]x = 69

(23/2)x = 69

23x = 69(2)

23x = 138

x = 6

to find y, let's insert the value of x into either the first or second equation:

x = 6
5x - 2y = - 42

5(6) - 2y = - 42

30 - 2y = - 42

- 2y = - 42 - 30

- 2y = - 72

2y = 72

y = 36


in conclusion:

x = 6
y = 36