Mathematics 10 — Exercise Review · Q5

Full question

Find the real values of x and y in the following vector equation.

Step-by-step solution

1. Group the î components and the ĵ components separately. Equal vectors have equal corresponding components.

   $$î\times \left(2\times x-1\right)+ĵ\times \left(y+5\right)=\frac{î}{4}-8\times ĵ$$

2. Equate the corresponding entries.

   $$2\times x-1=\frac{1}{4}$$

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

   $$2\times x=\frac{1}{4}+1$$

4. Simplify the constant calculation.

   $$2\times x=\frac{5}{4}$$

5. Divide both sides by the variable coefficient.

   $$x=\frac{5}{8}$$

6. Reduce the fraction.

   $$x=\frac{5}{8}$$

7. Equate the corresponding entries.

   $$y+5=-8$$

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

   $$y=-8-5$$

9. Simplify the constant calculation.

   $$y=-13$$

10. Divide both sides by the variable coefficient.

    $$y=-13\times \frac{1}{1}$$

11. Reduce the fraction.

    $$y=-13$$

12. Check the values in the original two matrices.

    $$(\left[\begin{array}{c}\frac{1}{4}\\ -8\end{array}\right],\left[\begin{array}{c}\frac{1}{4}\\ -8\end{array}\right])$$

Answer

The final answer is shown below.