Find x and y: x+y=7, 2x−y=5

The equation $x+y=72x-y=5$ implies:

$$x+y=5 \quad (1)$$ $$72x-y=5 \quad (2)$$

$$(x+y) + (72x-y) = 5+5$$ $$x+72x+y-y = 10$$ $$73x = 10$$

Divide both sides by 73.

$$x = \frac{10}{73}$$

$$x+y=5$$ $$\frac{10}{73}+y=5$$

Subtract $\frac{10}{73}$ from both sides.

$$y = 5 - \frac{10}{73}$$

To subtract, find a common denominator.

$$y = \frac{5 \times 73}{73} - \frac{10}{73}$$ $$y = \frac{365}{73} - \frac{10}{73}$$ $$y = \frac{365-10}{73}$$ $$y = \frac{355}{73}$$

The solutions are:

$$x = \frac{10}{73}, \quad y = \frac{355}{73}$$