Question

Solve the linear eqvations by matrix inversion method 2x -2y = 4 , 3x + 2y = 6​

Answer 1

The answer is below

Explanation:

A linear graph has an equation of the form:

y = mx + b,

where y and x are variables, m is the slope (rate of change) of the graph and b is the y intercept (value of y when x is 0).

Given that:

2x -2y = 4 , 3x + 2y = 6

The matrix form of the equation is:

AX = B

`A=\left[\begin{array}{cc}2&-2\\3&2\end{array}\right] ,X=\left[\begin{array}{c}x\\y\end{array}\right] ,B=\left[\begin{array}{c}4\\6\end{array}\right] \\\\Therefore:\\\\\left[\begin{array}{cc}2&-2\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}4\\6\end{array}\right] \\\\\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{cc}2&-2\\3&2\end{array}\right]^(-1) \left[\begin{array}{c}4\\6\end{array}\right] \\\\`

`\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{cc}0.2&0.2\\-0.3&0.2\end{array}\right] \left[\begin{array}{c}4\\6\end{array}\right] \\\\\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}2\\0\end{array}\right]`