Chapter 2.4A, Problem 6MCQ

To determine

To find: the value of x and y for the given matrix equations.

Answer to Problem 6MCQ

  $x=3,\text{ and }y=6$

Explanation of Solution

Given information:

The matrix equation is as follows:

  $\left[\begin{array}{l}y-3\\ y\end{array}\right]=\left[\begin{array}{l}x\\ 2x\end{array}\right]$

Calculation:

For the two matrices to be equal, they must equal on every coordinate. So, we get

  $\begin{array}{c}y-3=x\\ y=2x\end{array}$

Put the value $y=2x$ in first equation and solve as follows:

  $\begin{array}{c}y-3=x\\ 2x-3=x\\ 2x-x=3\\ x=3\end{array}$

Now put the value of x in $y=2x$ and solve as follows:

  $\begin{array}{c}y=2x\\ =2\left(3\right)\\ =6\end{array}$

Thus, the solution $\left(x,y\right)$ for the given system is $\left(3,6\right)$ .