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

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

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

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

(x = - 2, x = 1, y = - 2 y = 1)

Solution steps

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

Subtract the equations

y = - x^{2} + 2

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

Simplify

0 = - x^{2} + 2 - x

Solve

0 = - x^{2} + 2 - x : x = - 2, x = 1

Plug the solutions

x = - 2, x = 1

into

y = - x^{2} + 2

For

y = - x^{2} + 2

, subsitute

x

with

- 2 : y = - 2

For

y = - x^{2} + 2

, subsitute

x

with

1 : y = 1

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

(x = - 2, x = 1, y = - 2 y = 1)

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

x - y = 9, x \cdot y = 14

3 y + 43 = - 2, 5 x^{8} y - 12 x = 32

\frac{( a + 1 )}{5} = 1, \frac{6}{( b + 2 )} = c

x^{2} = 23 x + y, y^{2} = 23 x + y