Question

Use matrix method to find the point of intersection between the lines:

5x+3y-35=0 and 3x-4y=-8

Answer 1

Hello !

`\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}`

`\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}`

`\Leftrightarrow AX = B`

With

`A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right]`

`X=\left[\begin{array}{ccc}x\\y\\\end{array}\right]`

`B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right]`

The solution is given by
`X=A^(-1)B`.

`X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^( - 1) \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right]`

`X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right]`

The point of intersection between the lines is (4;5).

Have a nice day

Answer 2

Point of intersection (4,5)

Explanation:

5x + 3y - 35 = 0

3x - 4y = -8

⇒ 5x + 3y = 35

3x - 4y = -8

Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.

`\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right]`

`\sf B = \left[\begin{array}{c}35&-8\end{array}\right]`

AX = B

`\sf X =A^(-1)B`

`Now ,\ we \ have \ to \ find \ A^(-1)`,

Find the workout in the document attached.