What is x/2+y/3 =2,*x/4+y/2 =2 ?

The solution to x/2+y/3 =2,*x/4+y/2 =2 is

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x/2+y/3 =2,*x/4+y/2 =2

\frac{x}{2} + \frac{y}{3} = 2, \cdot \frac{x}{4} + \frac{y}{2} = 2

(x = 2, y = 3)

Solution steps

[\frac{x}{2} + \frac{y}{3} = 2 \frac{x}{4} + \frac{y}{2} = 2]

Isolate

x

for

\frac{x}{2} + \frac{y}{3} = 2 : x = 4 - \frac{2 y}{3}

Plug the solutions

x = 4 - \frac{2 y}{3}

into

\cdot \frac{x}{4} + \frac{y}{2} = 2

For

\cdot \frac{x}{4} + \frac{y}{2} = 2

, subsitute

x

with

4 - \frac{2 y}{3} : y = 3

Plug the solutions

y = 3

into

\frac{x}{2} + \frac{y}{3} = 2

For

\frac{x}{2} + \frac{y}{3} = 2

, subsitute

y

with

3 : x = 2

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{x}{2} + \frac{y}{3} = 2, \cdot \frac{x}{4} + \frac{y}{2} = 2

(x = 2, y = 3)

3 x + y = - 17, 5 x + 2 y = - 29

3 x - 2 y = 5, \frac{( 2 x )}{3} + \frac{y}{2} = - \frac{7}{9}

y = \frac{5}{7}, x = 1

2 x + y - 3 z = 4, x + 2 y - 6 z = 0, x - y + z = 0

5 x - 3 y = - 5, 2 x + 4 y = 24