What is x/2+y/3 =7, x/3+y/2 =8 ?

The solution to x/2+y/3 =7, x/3+y/2 =8 is x=6,y=12

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x/2+y/3 =7, x/3+y/2 =8

\frac{x}{2} + \frac{y}{3} = 7, \frac{x}{3} + \frac{y}{2} = 8

x = 6, y = 12

Solution steps

[\frac{x}{2} + \frac{y}{3} = 7 \frac{x}{3} + \frac{y}{2} = 8]

Isolate

x

for

\frac{x}{2} + \frac{y}{3} = 7 : x = 14 - \frac{2 y}{3}

Substitute

x = 14 - \frac{2 y}{3}

[\frac{14 - \frac{2 y}{3}}{3} + \frac{y}{2} = 8]

Simplify

[\frac{84 + 5 y}{18} = 8]

Isolate

y

for

\frac{84 + 5 y}{18} = 8 : y = 12

For

x = 14 - \frac{2 y}{3}

Substitute

y = 12

x = 14 - \frac{2 \cdot 12}{3}

14 - \frac{2 \cdot 12}{3} = 6

x = 6

The solutions to the system of equations are:

x = 6, y = 12

\frac{2}{5} x + \frac{3}{5} y = 3, 7 x - y = 30

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

3 x - 5 y = 30, 3 x - 2 y = 21

4 x + y = - 3, - 3 x + y = 11

8 x - 3 y = 18, - 2 x + 9 y = 12

What is x/2+y/3 =7, x/3+y/2 =8 ?
The solution to x/2+y/3 =7, x/3+y/2 =8 is x=6,y=12