What is 6x^2+y=1,412x^2-y=4 ?

The solution to 6x^2+y=1,412x^2-y=4 is

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6x^2+y=1,412x^2-y=4

6 x^{2} + y = 1, 412 x^{2} - y = 4

x = \frac{5}{418}, x = - \frac{5}{418}, y = \frac{194}{209} y = \frac{194}{209}

Solution steps

[6 x^{2} + y = 1 412 x^{2} - y = 4]

Add the equations

6 x^{2} + y = 1

6 x^{2} + y + (412 x^{2} - y) = 1 + 4

Simplify

418 x^{2} = 5

Solve

418 x^{2} = 5 : x = \frac{5}{418}, x = - \frac{5}{418}

Plug the solutions

x = \frac{5}{418}, x = - \frac{5}{418}

into

6 x^{2} + y = 1

For

6 x^{2} + y = 1

, subsitute

x

with

\frac{5}{418} : y = \frac{194}{209}

For

6 x^{2} + y = 1

, subsitute

x

with

- \frac{5}{418} : y = \frac{194}{209}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

6 x^{2} + y = 1, 412 x^{2} - y = 4

are

x = \frac{5}{418}, x = - \frac{5}{418}, y = \frac{194}{209} y = \frac{194}{209}

abb = 6 c, c = 10

x + y = 1, 1 x y = 30

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

2 x + 3 y = 7, 3 x - 2 y = 4

x + y = 2 x y, x - y = x y