What is 1/5 x+1/6 y=12, 1/3 x-1/7 y=8 ?

The solution to 1/5 x+1/6 y=12, 1/3 x-1/7 y=8 is x= 1920/53 ,y= 1512/53

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1/5 x+1/6 y=12, 1/3 x-1/7 y=8

\frac{1}{5} x + \frac{1}{6} y = 12, \frac{1}{3} x - \frac{1}{7} y = 8

x = \frac{1920}{53}, y = \frac{1512}{53}

Solution steps

[\frac{1}{5} x + \frac{1}{6} y = 12 \frac{1}{3} x - \frac{1}{7} y = 8]

Isolate

x

for

\frac{1}{5} x + \frac{1}{6} y = 12 : x = 60 - \frac{5}{6} y

Substitute

x = 60 - \frac{5}{6} y

[\frac{1}{3} (60 - \frac{5}{6} y) - \frac{1}{7} y = 8]

Simplify

[\frac{2520 - 53 y}{126} = 8]

Isolate

y

for

\frac{2520 - 53 y}{126} = 8 : y = \frac{1512}{53}

For

x = 60 - \frac{5}{6} y

Substitute

y = \frac{1512}{53}

x = 60 - \frac{5}{6} \cdot \frac{1512}{53}

60 - \frac{5}{6} \cdot \frac{1512}{53} = \frac{1920}{53}

x = \frac{1920}{53}

The solutions to the system of equations are:

x = \frac{1920}{53}, y = \frac{1512}{53}

x + y = 7, x - 2 y = 1

5 x + y = 2, 7 x - y = 3

3 y - 6 x = 9, 2 x + y = - 2

3 x + 2 y - 7 = 2, x + y - 6 = 0

3 x + 3 y = 21, 3 x - 3 y = 3

What is 1/5 x+1/6 y=12, 1/3 x-1/7 y=8 ?
The solution to 1/5 x+1/6 y=12, 1/3 x-1/7 y=8 is x= 1920/53 ,y= 1512/53