Mathematics 10 — Exercise 6.2 · Q3 (i)

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.

   $$\left[\begin{array}{c}x+2\\ y+3\end{array}\right]=\left[\begin{array}{c}7\\ 6\end{array}\right]$$

2. Equate the corresponding entries.

   $$x+2=7$$

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

   $$x=7-2$$

4. Simplify the constant calculation.

   $$x=5$$

5. Divide both sides by the variable coefficient.

   $$x=5\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=5$$

7. Equate the corresponding entries.

   $$y+3=6$$

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

   $$y=6-3$$

9. Simplify the constant calculation.

   $$y=3$$

10. Divide both sides by the variable coefficient.

    $$y=3\times \frac{1}{1}$$

11. Reduce the fraction.

    $$y=3$$

12. Check the values in the original two matrices.

    $$(\left[\begin{array}{c}7\\ 6\end{array}\right],\left[\begin{array}{c}7\\ 6\end{array}\right])$$

Answer

The final answer is shown below.