Question

Solve:(1/7)x +(1/6)y =3 ; (1/2)x - (1/3)y =5​

Answer 1

(14, 6 )

Explanation:

Given

`(1)/(7)` x +
`(1)/(6)` y = 3 ( multiply through by 42 to clear the fractions )

6x + 7y = 126 → (1)

`(1)/(2)` x -
`(1)/(3)` y = 5 ( multiply through by 6 to clear the fractions )

3x - 2y = 30 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 6x + 4y = - 60 → (3)

Add (1) and (3)term by term to eliminate x

11y = 66 ( divide both sides by 11 )

y = 6

Substitute y = 6 into either of the 2 equations and evaluate for x

Substituting into (1)

6x + 7(6) = 126

6x + 42 = 126 ( subtract 42 from both sides )

6x = 84 ( divide both sides by 6 )

x = 14

Solution is (14, 6 )