What is 1/7 x+1/6 y=3, 1/2 x+1/3 y=2 ?

The solution to 1/7 x+1/6 y=3, 1/2 x+1/3 y=2 is x=-56/3 ,y=34

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1/7 x+1/6 y=3, 1/2 x+1/3 y=2

\frac{1}{7} x + \frac{1}{6} y = 3, \frac{1}{2} x + \frac{1}{3} y = 2

x = - \frac{56}{3}, y = 34

Solution steps

[\frac{1}{7} x + \frac{1}{6} y = 3 \frac{1}{2} x + \frac{1}{3} y = 2]

Isolate

x

for

\frac{1}{7} x + \frac{1}{6} y = 3 : x = 21 - \frac{7}{6} y

Substitute

x = 21 - \frac{7}{6} y

[\frac{1}{2} (21 - \frac{7}{6} y) + \frac{1}{3} y = 2]

Simplify

[\frac{42 - y}{4} = 2]

Isolate

y

for

\frac{42 - y}{4} = 2 : y = 34

For

x = 21 - \frac{7}{6} y

Substitute

y = 34

x = 21 - \frac{7}{6} \cdot 34

21 - \frac{7}{6} \cdot 34 = - \frac{56}{3}

x = - \frac{56}{3}

The solutions to the system of equations are:

x = - \frac{56}{3}, y = 34

x + y = - 4, - x + 2 y = 13

x - y = 28, x - 3 y = 10

2 x - y = 4, - 10 x + 5 y = 0

3 x + y = 5, 2 x - y = 0

a = 6, b = 4, c = 7

What is 1/7 x+1/6 y=3, 1/2 x+1/3 y=2 ?
The solution to 1/7 x+1/6 y=3, 1/2 x+1/3 y=2 is x=-56/3 ,y=34