Question

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

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

Answer:

Point of intersection (4,5)

Step-by-step 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.