What is 1/2 x+1/3 y=2, 1/3 x+1/2 y= 13/6 ?

The solution to 1/2 x+1/3 y=2, 1/3 x+1/2 y= 13/6 is x=2,y=3

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1/2 x+1/3 y=2, 1/3 x+1/2 y= 13/6

\frac{1}{2} x + \frac{1}{3} y = 2, \frac{1}{3} x + \frac{1}{2} y = \frac{13}{6}

x = 2, y = 3

Solution steps

[\frac{1}{2} x + \frac{1}{3} y = 2 \frac{1}{3} x + \frac{1}{2} y = \frac{13}{6}]

Isolate

x

for

\frac{1}{2} x + \frac{1}{3} y = 2 : x = 4 - \frac{2}{3} y

Substitute

x = 4 - \frac{2}{3} y

[\frac{1}{3} (4 - \frac{2}{3} y) + \frac{1}{2} y = \frac{13}{6}]

Simplify

[\frac{24 + 5 y}{18} = \frac{13}{6}]

Isolate

y

for

\frac{24 + 5 y}{18} = \frac{13}{6} : y = 3

For

x = 4 - \frac{2}{3} y

Substitute

y = 3

x = 4 - \frac{2}{3} \cdot 3

4 - \frac{2}{3} \cdot 3 = 2

x = 2

The solutions to the system of equations are:

x = 2, y = 3

x = 2 y + 6, y = 2 x - 3

2 x + y + z = 4, x - 3 y - 2 z = - 4, 4 x + y - 3 z = 2

7 m + 7 n = 11, 27 m + 6 n = 108

7 x + 10 y = 3, 6 y = 2 x + 9

5 x + 6 y = 20, 3 x + 8 y = 34

What is 1/2 x+1/3 y=2, 1/3 x+1/2 y= 13/6 ?
The solution to 1/2 x+1/3 y=2, 1/3 x+1/2 y= 13/6 is x=2,y=3