What is 2x+5 y/x y=6,4x-5 y/x y=-3 ?

The solution to 2x+5 y/x y=6,4x-5 y/x y=-3 is

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2x+5 y/x y=6,4x-5 y/x y=-3

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

(x = \frac{1}{2}, x = \frac{1}{2}, y = \frac{1}{2} y = - \frac{1}{2})

Solution steps

[2 x + 5 \cdot \frac{y}{x} y = 6 4 x - 5 \cdot \frac{y}{x} y = - 3]

Add the equations

2 x + 5 \frac{y}{x} y = 6

2 x + 5 \cdot \frac{y}{x} y + (4 x - 5 \cdot \frac{y}{x} y) = 6 + (- 3)

Simplify

6 x = 3

Solve

6 x = 3 : x = \frac{1}{2}

Plug the solutions

x = \frac{1}{2}

into

2 x + 5 \frac{y}{x} y = 6

For

2 x + 5 \frac{y}{x} y = 6

, subsitute

x

with

\frac{1}{2} : y = \frac{1}{2}, y = - \frac{1}{2}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

(x = \frac{1}{2}, x = \frac{1}{2}, y = \frac{1}{2} y = - \frac{1}{2})

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

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

y = 2 x^{2} + z^{2}, y = 6 - 2 x^{2} - z^{2}

\frac{1}{2 ^{x}} + \frac{2}{3 ^{y}} = 10, \frac{3}{2 ^{x}} + \frac{7}{3 ^{y}} = 33

a + b = 27, a \cdot b = 182

What is 2x+5 y/x y=6,4x-5 y/x y=-3 ?
The solution to 2x+5 y/x y=6,4x-5 y/x y=-3 is