# Chapter 12

## Section 1

### 3

#### a)

Note: The answer printed in the book is given as $(\frac{7}{8}, \frac{11}{8})$. This is incorrect!

If the two lines $y_1 = -2x + 5, \,$ and $y_2 = 5x - 3\,$ intersect, then $y_1 = y_2\,$. Therefore:

$y_1 - y_2 = (-2x + 5) - (5x - 3) = 0 \,$

$-7x + 8 = 0 \,$

$-7x = -8 \,$

$x = \frac{8}{7}$

Thus, we can now plug in the value for x into any one of our two equations to find the point of interception:

$y_2 = 5 \cdot \frac{8}{7} - 3 = \frac{40}{7} - 3 = \frac{19}{7}$

Thus, the point of interception is $\left(\frac{8}{7}, \frac{19}{7} \right)$.