Write the given matrix equation as a system of linear equations without matrices. begin{bmatrix}3 & 0 -3 &1 end{bmatrix}begin{bmatrix}x y end{bmatrix}=begin{bmatrix}6 -7 end{bmatrix}

Question
Matrices
Write the given matrix equation as a system of linear equations without matrices. $$\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}$$

2021-02-26
Step 1
Given: $$\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}$$
Step 2
Now, $$\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}$$
$$\therefore 3x+0\cdot y =6 \ \ \ \ \ \ \ (1)$$
$$-3x+1y =7 \ \ \ \ \ \ \ (2)$$
From equation (1) , we have
$$\Rightarrow 3x=6$$
$$\Rightarrow x=\frac{6}{3}$$
$$\Rightarrow x=3$$
Putting x=2 in equation (2) , we have
$$-3(2)+1y=7$$
$$\Rightarrow -6+y=7$$
$$\Rightarrow y=7+6$$
$$\Rightarrow y=13$$
Answer: Therefore the values of x and y are 2 and 13 respectively

Relevant Questions

Write the given matrix equation as a system of linear equations without matrices.
$$\begin{bmatrix}4 & -7 \\ 2 &-3 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}-3 \\1 \end{bmatrix}$$
Write the matrix equation as a system of linear equations without matrices.
$$\begin{bmatrix}2 & 0&-1 \\0 & 3&0\\1&1&0 \end{bmatrix}\begin{bmatrix}x \\ y \\z \end{bmatrix}=\begin{bmatrix}6 \\ 9\\5 \end{bmatrix}$$
Write the given matrix equation as a system of linear equations without matrices.
$$\begin{bmatrix}-1 & 0&1 \\ 0 & -1 &0 \\ 0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}$$
Write the matrix equation as a system of linear equations without matrices.
$$\begin{bmatrix}-1 & 0&1 \\0 & -1&0\\0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\z \end{bmatrix}=\begin{bmatrix}-4 \\ 2\\4 \end{bmatrix}$$
The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or $$x_1,x_2,x_3, x_4$$
(b) Determine whether the system is consistent. If it is consistent, give the solution.
$$\begin{matrix}1 & 0 & 3 & 0 &1 \\ 0 & 1 & 4 & 3&2\\0&0&1&2&3\\0&0&0&0&0 \end{matrix}$$
write B as a linear combination of the other matrices, if possible.
$$B=\begin{bmatrix}2 & 3 \\-4 & 2 \end{bmatrix} , A_1=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &-1 \\1 & 0 \end{bmatrix} , A_3=\begin{bmatrix}1 &1 \\0 & 1 \end{bmatrix}$$
write B as a linear combination of the other matrices, if possible.
$$B=\begin{bmatrix}2 & 5 \\0 & 3 \end{bmatrix} , A_1=\begin{bmatrix}1 & 2 \\-1 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &1 \\2 & 1 \end{bmatrix}$$
The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or $$x_1,x_2,x_3, x_4$$
(b) Determine whether the system is consistent. If it is consistent, give the solution.
$$\begin{matrix}1 & 0 & 2 & -1 \\ 0 & 1 & -4 & -2\\0&0&0&0&0 \end{matrix}$$
$$[(2,0,-1),(0,3,0),(1,1,0)][(x),(y),(z)]=[(6),(9),(5)]$$
$$A=\begin{bmatrix}5 & 3 \\ -3 & -1 \\ -2 & -5 \end{bmatrix} \text{ and } B=\begin{bmatrix}0 & -2 \\ 1 & 3 \\ 4 & -3 \end{bmatrix}$$