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Solve the system of equations x/6+y/8 =14 and x/8+y/6 =14

Solution

\frac{x}{6} + \frac{y}{8} = 14, \frac{x}{8} + \frac{y}{6} = 14

Solution

x = 48, y = 48

Solution steps

[\frac{x}{6} + \frac{y}{8} = 14 \frac{x}{8} + \frac{y}{6} = 14]

Isolate

x

for

\frac{x}{6} + \frac{y}{8} = 14 : x = 84 - \frac{3 y}{4}

Substitute

x = 84 - \frac{3 y}{4}

[\frac{84 - \frac{3 y}{4}}{8} + \frac{y}{6} = 14]

Simplify

[\frac{1008 + 7 y}{96} = 14]

Isolate

y

for

\frac{1008 + 7 y}{96} = 14 : y = 48

For

x = 84 - \frac{3 y}{4}

Substitute

y = 48

x = 84 - \frac{3 \cdot 48}{4}

84 - \frac{3 \cdot 48}{4} = 48

x = 48

The solutions to the system of equations are:

x = 48, y = 48

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The solution to Solve the system of equations x/6+y/8 =14 and x/8+y/6 =14 is x=48,y=48