Answer:
x = -6, y = 27
Step-by-step explanation:
For the top equation;
[tex] \frac{x + y}{2} - \frac{x - y}{6} = 16[/tex]
[tex]3(x + y) - (x - y) = 96[/tex]
[tex]3x + 3y - x - y = 96[/tex]
[tex]2x + 4y = 96[/tex]
[tex]x + 2y = 48[/tex]
For the bottom equation:
[tex] \frac{x}{3} + \frac{x + 2y}{3} = 14[/tex]
[tex]x + x + 2y = 42[/tex]
[tex]2x + 2y = 42[/tex]
[tex]x + y = 21[/tex]
Eliminating x by subtracting the two resulting equations, we have y = 27, and it follows that x = -6.
