Solutions of Equations

Algebra Level 2

$\large \begin{aligned} x+y^2 & =2x \\ x+y & =2y^2 \end{aligned}$

Solve the system of equations above.

(5,-2)

and

(-2,3)

(1,2)

and

(0,-1)

(2,3)

and

(5,-5)

(1,1)

and

(0,0)

2 solutions

Ryan Shi
Sep 13, 2016

Correct me if I'm wrong, but I just did:

$x + y^2 = 2x$

$y^2 = x$ ...... Equation 1

$x + y = 2y^2$

$x + y = 2x$ ...... From Equation 1

$Hence$ $y = x$

Out of the four answers only $(1,1)$ and $(0,0)$ has property $y = x$

Viki Zeta
Sep 12, 2016

$x + y^2 = 2x \\ 2x - x = y^2 \\ x = y^2 \\ x + y = 2y^2 \\ y^2 + y = 2y^2 \\ y^2 = y \\ y^2 - y = 0 \\ y(y-1) = 0 \\ \fbox{ y = 0, y = 1 } \\ \fbox{ y = 1 } \\ \implies x = y^2 \implies x = 0 \\ \fbox{ y = 0 } \\ \implies x = 1^2 = 1$

Solutions of Equations

2 solutions

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