Answer:
(14, 9 )
Step-by-step explanation:
Given
[tex]\frac{x}{7}[/tex] + [tex]\frac{y}{3}[/tex] = 5 ( multiply through by 21 to clear the fractions )
3x + 7y = 105 → (1)
[tex]\frac{x}{2}[/tex] - [tex]\frac{y}{9}[/tex] = 6 ( multiply through by 18 to clear the fractions )
9x - 2y = 108 → (2)
Multiplying (1) by - 3 and adding to (2) eliminates the term in x
- 9x - 21y = - 315 → (3)
Add (2) and (3) term by term to eliminate x
- 23y = - 207 ( divide both sides by - 23 )
y = 9
Substitute y = 9 into either of the 2 equations and evaluate for x
Substituting into (1)
3x + 7(9) = 105
3x + 63 = 105 ( subtract 63 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Solution is (14, 9 )
