Solve Simultaneously

You've done simultaneous equations and surds, but have you done them together?

Warm-up:

The equations imply that $x, y > 0$ .
Both equations have integers on the RHS
implying $x, y, \sqrt{x}, \sqrt{y}$ are elements of the integers
moreover $x, y$ are perfect squares
so $0 < x < 7$ and $0 < y < 11$ .
So $x \in {1, 4}$ and $y \in {1, 4, 9}$ .
Therefore $x = 4$ and $y = 9$
Are there any other solutions?

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Simultaneous Equations with Roots

Warm-up:

Surds

Simultaneous
Equations

Solution:

Simultaneous Equations with Roots

Warm-up:

Surds

SimultaneousEquations

Solve Simultaneously

Solution:

Simultaneous
Equations