Question

1/2x +1/3y=2 and 1/3x+1/2y=13/6 what is the value of x and y ​

Answer 1

Answer:

x = 2, y = 3

Step-by-step explanation:

See, there are two equations

$\left \{{\frac{1}{2}x + \frac{1}{3}y=2} - (1) \atop{\frac{1}{3}x + \frac{1}{2}y=\frac{13}{6}} - (2)} \right.$

Finding the value of x in (1),

$\frac{1}{2}x + \frac{1}{3}y =2$

$\frac{1}{2}x = 2 - \frac{1}{3}y$

∴ $x = 2(2 - \frac{1}{3}y) = 4 - \frac{2}{3}y$

Now 4 - 2/3y - (3)

Sub (3) in (2),

$\frac{1}{3}(4 - \frac{2}{3}y) + \frac{1}{2}y = \frac{13}{6}$ ( 4-2/3y came from x's value)

Solving the above equation, we will get

$y = 3 - (4)$

Then sub (4) into (1)

$\frac{1}{2}x + \frac{1}{3}(3) = 2$

∴ x = 2