Answer:
(12, 6 )
Step-by-step explanation:
Given the 2 equations
[tex]\frac{x}{3}[/tex] - [tex]\frac{y}{2}[/tex] = 1 ( multiply through by 6 to clear the fractions )
2x - 3y = 6 → (1)
[tex]\frac{x}{4}[/tex] - [tex]\frac{y}{3}[/tex] = 1 ( multiply through by 12 to clear the fractions )
3x - 4y = 12 → (2)
Multiplying (1) by 3 and (2) by - 2 and adding the result will eliminate x
6x - 9y = 18 → (3)
- 6x + 8y = - 24 → (4)
Add (3) and (4) term by term to eliminate x
0 - y = - 6
- y = - 6 ( multiply both sides by - 1 )
y = 6
Substitute y = 6 into either of the 2 equations and solve for x
Substituting into (1)
2x - 3( 6) = 6
2x - 18 = 6 (add 18 to both sides )
2x = 24 ( divide both sides by 2 )
x = 12
solution is (12, 6 )
