What is 4/x+3/y =1, 8/x-9/y =7 ?

The solution to 4/x+3/y =1, 8/x-9/y =7 is

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4/x+3/y =1, 8/x-9/y =7

\frac{4}{x} + \frac{3}{y} = 1, \frac{8}{x} - \frac{9}{y} = 7

(x = 2, y = - 3)

Solution steps

[\frac{4}{x} + \frac{3}{y} = 1 \frac{8}{x} - \frac{9}{y} = 7]

Isolate

x

for

\frac{4}{x} + \frac{3}{y} = 1 : x = - \frac{4 y}{3 - y}; y \neq = 3

Plug the solutions

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

into

\frac{8}{x} - \frac{9}{y} = 7

For

\frac{8}{x} - \frac{9}{y} = 7

, subsitute

x

with

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

Plug the solutions

y = - 3

into

\frac{4}{x} + \frac{3}{y} = 1

For

\frac{4}{x} + \frac{3}{y} = 1

, subsitute

y

with

- 3 : x = 2

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{4}{x} + \frac{3}{y} = 1, \frac{8}{x} - \frac{9}{y} = 7

(x = 2, y = - 3)

x - 2 y = 5, 3 x + y = 9

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

5 x + 3 y = 21, x + 2 y = 12

2 \frac{x}{a} + \frac{y}{b} = 2, \frac{x}{a} - \frac{y}{b} = 4

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