What is 3x+y=11,2xy=5 ?

The solution to 3x+y=11,2xy=5 is

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3x+y=11,2xy=5

3 x + y = 11, 2 x y = 5

(x = \frac{11 + 91}{6}, x = \frac{11 - 91}{6}, y = - \frac{- 11 + 91}{2} y = \frac{11 + 91}{2})

Solution steps

[3 x + y = 11 2 x y = 5]

Isolate

x

for

3 x + y = 11 : x = \frac{11 - y}{3}

Plug the solutions

x = \frac{11 - y}{3}

into

2 x y = 5

For

2 x y = 5

, subsitute

x

with

\frac{11 - y}{3} : y = - \frac{- 11 + 91}{2}, y = \frac{11 + 91}{2}

Plug the solutions

y = - \frac{- 11 + 91}{2}, y = \frac{11 + 91}{2}

into

3 x + y = 11

For

3 x + y = 11

, subsitute

y

with

- \frac{- 11 + 91}{2} : x = \frac{11 + 91}{6}

For

3 x + y = 11

, subsitute

y

with

\frac{11 + 91}{2} : x = \frac{11 - 91}{6}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

3 x + y = 11, 2 x y = 5

are

(x = \frac{11 + 91}{6}, x = \frac{11 - 91}{6}, y = - \frac{- 11 + 91}{2} y = \frac{11 + 91}{2})

5 x + 3 y = 8, - 5 x - 3 y = 7

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

d (ab) a = 4, b = 7

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

x - 2 y = 6, x - 2 y = 4