Solutions To Mathematics Textbooks/Basic Mathematics/Chapter 12

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Chapter 12[edit]

Section 1[edit]

3[edit]

a)[edit]

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).