What is x+3y^2=5,3x-y=5y ?

The solution to x+3y^2=5,3x-y=5y is

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

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

(x = 2, x = - \frac{10}{3}, y = 1 y = - \frac{5}{3})

Solution steps

[x + 3 y^{2} = 5 3 x - y = 5 y]

Isolate

y

for

3 x - y = 5 y : y = \frac{x}{2}

Plug the solutions

y = \frac{x}{2}

into

x + 3 y^{2} = 5

For

x + 3 y^{2} = 5

, subsitute

y

with

\frac{x}{2} : x = 2, x = - \frac{10}{3}

Plug the solutions

x = 2, x = - \frac{10}{3}

into

3 x - y = 5 y

For

3 x - y = 5 y

, subsitute

x

with

2 : y = 1

For

3 x - y = 5 y

, subsitute

x

with

- \frac{10}{3} : y = - \frac{5}{3}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

(x = 2, x = - \frac{10}{3}, y = 1 y = - \frac{5}{3})

(a - b) (a + b) = 16, a + b = 8

f (x) = 0, f (x) = x^{3} - 3 x^{2} + 4

d = 300 m, t = 3 h

c = (a + b) + c, a = 6

2 x + 3 y = 9, (a + b) x + (2 a - b) y = 3 (a + b + 1)