What is x+3y=13,x^2+3y^2=43 ?

The solution to x+3y=13,x^2+3y^2=43 is

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x+3y=13,x^2+3y^2=43

x + 3 y = 13, x^{2} + 3 y^{2} = 43

(x = \frac{5}{2}, x = 4, y = \frac{7}{2} y = 3)

Solution steps

[x + 3 y = 13 x^{2} + 3 y^{2} = 43]

Isolate

x

for

x + 3 y = 13 : x = 13 - 3 y

Plug the solutions

x = 13 - 3 y

into

x^{2} + 3 y^{2} = 43

For

x^{2} + 3 y^{2} = 43

, subsitute

x

with

13 - 3 y : y = \frac{7}{2}, y = 3

Plug the solutions

y = \frac{7}{2}, y = 3

into

x + 3 y = 13

For

x + 3 y = 13

, subsitute

y

with

\frac{7}{2} : x = \frac{5}{2}

For

x + 3 y = 13

, subsitute

y

with

3 : x = 4

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x + 3 y = 13, x^{2} + 3 y^{2} = 43

are

(x = \frac{5}{2}, x = 4, y = \frac{7}{2} y = 3)

u (y, x) - 9 u (y, x) = (\frac{1}{2}) x^{4}, y = 6

0 + \frac{1}{2} yy = x + 150, x = 15

x + y = 12, \frac{1}{x} + \frac{1}{y} = 8

8 x + (- 2 a + b - 4) = 4 y, - 6 x + (a - b + 2) y + 9 = 0

3 x y + 2 y^{2} = 5, x y - 3 y^{2} = - 57