Chapter 12

Section 1

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

If the two lines $y_{1} = - 2 x + 5,$ and $y_{2} = 5 x - 3$ intersect, then $y_{1} = y_{2}$ . Therefore:

$y_{1} - y_{2} = (- 2 x + 5) - (5 x - 3) = 0$

$- 7 x + 8 = 0$

$- 7 x = - 8$

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

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 $(\frac{8}{7}, \frac{19}{7})$ .