Question

Solve the system of linear equations using matrices.Х -3y=33x– 9y= 5

Answer 1

The system of equation is

x - 3y = 3

3x - 9y = 5

`\begin{bmatrix}{1} & {-3} & {} \\ {3} & {-9} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{3} & {} & {} \\ {5} & {} & {} \\ {} & {} & {}\end{bmatrix}`

We will divide the second roe by 3 to make the first number 1

`\begin{bmatrix}{1} & {-3} & {} \\ {(3)/(3)} & {-(9)/(3)} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{(3)/(3)} & {} & {} \\ {(5)/(3)} & {} & {} \\ {} & {} & {}\end{bmatrix}`
`\begin{bmatrix}{1} & {-3} & {} \\ {1} & {-3} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{1} & {} & {} \\ {(5)/(3)} & {} & {} \\ {} & {} & {}\end{bmatrix}`

Since the second column has the same numbers, that means there is no solution for this equation because -3 + -3 = 0 means x and y will disappear from the equations

Since 1 not equal 5/3 that means the two lines are parallel

If the two answers are equal that means the two lines coincide (over each other)