What is 4/x+3/y =2,4x+3y=25 ?

The solution to 4/x+3/y =2,4x+3y=25 is

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4/x+3/y =2,4x+3y=25

\frac{4}{x} + \frac{3}{y} = 2, 4 x + 3 y = 25

(x = 4, x = \frac{25}{8}, y = 3 y = \frac{25}{6})

Solution steps

[\frac{4}{x} + \frac{3}{y} = 2 4 x + 3 y = 25]

Isolate

x

for

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

Plug the solutions

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

into

4 x + 3 y = 25

For

4 x + 3 y = 25

, subsitute

x

with

- \frac{4 y}{3 - 2 y} : y = 3, y = \frac{25}{6}

Plug the solutions

y = 3, y = \frac{25}{6}

into

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

For

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

, subsitute

y

with

3 : x = 4

For

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

, subsitute

y

with

\frac{25}{6} : x = \frac{25}{8}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

\frac{4}{x} + \frac{3}{y} = 2, 4 x + 3 y = 25

are

(x = 4, x = \frac{25}{8}, y = 3 y = \frac{25}{6})

x y = 1, 2 (x - 1) (y + 2) = 15

y = x^{2} - 2 x + 3, y = - 5 x + 1

2 x + 5 \frac{y}{x} y = 6, 4 x - 5 \frac{y}{x} y = - 3

3 x + 5 y = 3, 2 x^{1} y = - 5

x - 1 = 1, x^{3} - y^{3} = 7