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

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

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

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

x = 2 - i \frac{2}{5}, x = 2 + i \frac{2}{5}, y = 1 + i \frac{2 10}{5} y = 1 - i \frac{2 10}{5}

Solution steps

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

Isolate

x

for

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

Plug the solutions

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

into

x^{2} + y^{2} = 3

For

x^{2} + y^{2} = 3

, subsitute

x

with

\frac{5 - y}{2} : y = 1 + i \frac{2 10}{5}, y = 1 - i \frac{2 10}{5}

Plug the solutions

y = 1 + i \frac{2 10}{5}, y = 1 - i \frac{2 10}{5}

into

2 x + y = 5

For

2 x + y = 5

, subsitute

y

with

1 + i \frac{2 10}{5} : x = 2 - i \frac{2}{5}

For

2 x + y = 5

, subsitute

y

with

1 - i \frac{2 10}{5} : x = 2 + i \frac{2}{5}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

x = 2 - i \frac{2}{5}, x = 2 + i \frac{2}{5}, y = 1 + i \frac{2 10}{5} y = 1 - i \frac{2 10}{5}

2 x - y = 3, x^{2} - x y = - 4

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

(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