What is 1/2*x+1/3*y=3,x+1/2*y=5 ?

The solution to 1/2*x+1/3*y=3,x+1/2*y=5 is x=2,y=6

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1/2x+1/3y=3,x+1/2*y=5

\frac{1}{2} \cdot x + \frac{1}{3} \cdot y = 3, x + \frac{1}{2} \cdot y = 5

x = 2, y = 6

Solution steps

[\frac{1}{2} x + \frac{1}{3} y = 3 x + \frac{1}{2} y = 5]

Isolate

x

for

\frac{1}{2} \cdot x + \frac{1}{3} \cdot y = 3 : x = 6 - \frac{2}{3} y

Substitute

x = 6 - \frac{2}{3} y

[6 - \frac{2}{3} y + \frac{1}{2} y = 5]

Simplify

[6 - \frac{1}{6} y = 5]

Isolate

y

for

6 - \frac{1}{6} y = 5 : y = 6

For

x = 6 - \frac{2}{3} y

Substitute

y = 6

x = 6 - \frac{2}{3} \cdot 6

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

x = 2

The solutions to the system of equations are:

x = 2, y = 6

- \frac{1}{8} \cdot x + y = \frac{33}{4}, - \frac{1}{9} \cdot x - \frac{1}{10} \cdot y = - \frac{47}{30}

9 x + 3 y = 33, 3 x + 9 y = 51

16 x + 11 y = 15, 411 x + 16 y = 89

3 x + y = 9, x - 2 y = - 4

2 x - 7 y = 6, 8 x - 28 y = 24

What is 1/2*x+1/3*y=3,x+1/2*y=5 ?
The solution to 1/2*x+1/3*y=3,x+1/2*y=5 is x=2,y=6