Question

37. Solve by inverse matrix method:
(i) 2x – 3y = 1 ; x + 5y = 7.​

Answer 1

GIVEN :

Solve by inverse matrix method :

(i) 2x - 3y = 1 ; x + 5y = 7.​

TO FIND :

The values of x and y

SOLUTION :

Given equations are

2x - 3y = 1 ;

x + 5y = 7

It is of the form AX=B

By using the  inverse matrix method we can solve the given equations as below :

AX=B

We can write it as $X=A^{-1}B$

Where $A=\left[\begin{array}{cc}2&-3\\1&5\end{array}\right]$

and $B=\left[\begin{array}{c}1\\7\end{array}\right]$

The formula is  $A^{-1}=\frac{adjA}{|A|}$

$|A|=\left|\begin{array}{cc}2&-3\\1&5\end{array}\right|$

=10-(-3)

=10+3

=13

|A|=13

Now $adjA=\left[\begin{array}{cc}5&3\\-1&2\end{array}\right]$  

We have that $X=A^{-1}B$

Substitute the matrices we get,

$\left[\begin{array}{c}x\\y\end{array}\right]=\frac{\left[\begin{array}{cc}5&3\\-1&2\end{array}\right]}{13}\times \left[\begin{array}{c}1\\7\end{array}\right]$

$=\frac{\left[\begin{array}{c}5+21\\-1+14\end{array}\right]}{13}$

$=\frac{\left[\begin{array}{c}26\\13\end{array}\right]}{13}$

$=\left[\begin{array}{c}2\\1\end{array}\right]$

$\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}2\\1\end{array}\right]$

⇒ the values are x=2 and y=1

Answer 2

Step-by-step explanation:

Solve the equation by matrix method. 2x - 3y = 1

x + 5y = 7