Solutions To Mathematics Textbooks/Basic Mathematics/Chapter 12

= Chapter 12 =

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