Mathematics 10 — Exercise 6.2 · Q3 (ii)

Full question

Find x and y in the following vector equation.

Step-by-step solution

1. Collect the î components together and the ĵ components together. Equality of vectors requires matching components.

   $$\left[\begin{array}{c}x+3\\ 0\end{array}\right]=\left[\begin{array}{c}-8\\ y\end{array}\right]$$

2. Equate the corresponding entries.

   $$x+3=-8$$

3. Collect the variable terms on the left and constants on the right.

   $$x=-8-3$$

4. Simplify the constant calculation.

   $$x=-11$$

5. Divide both sides by the variable coefficient.

   $$x=-11\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=-11$$

7. Equate the corresponding entries.

   $$0=y$$

8. Collect the variable terms on the left and constants on the right.

   $$-y=0+0$$

9. Simplify the constant calculation.

   $$-y=0$$

10. Divide both sides by the variable coefficient.

    $$y=\frac{0}{-1}$$

11. Reduce the fraction.

    $$y=0$$

12. Check the values in the original two matrices.

    $$(\left[\begin{array}{c}-8\\ 0\end{array}\right],\left[\begin{array}{c}-8\\ 0\end{array}\right])$$

Answer

The final answer is shown below.