Question

solve the following simultaneous linear equations using Matrix inversion method 3x±4y=8,x-6y=10
​

Answer 1

Given :  3x + 4y  = 8

x  - 6y = 10

To Find : Solve using Matrix inversion method

Solution:

3x + 4y  = 8

x  - 6y = 10

3x - 18y = 30

=> 22y = - 22

=> y = - 1

=> x = 4

Matrix inversion method

3x + 4y  = 8

x  - 6y = 10

$\left[\begin{array}{ccc}3&4 \\1&-6 \end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\10\end{array}\right]$

Det = 3 * (-6) - 1(4) = - 22

Inverse Exist

$Adj A = \left[\begin{array}{ccc}-6&-4 \\-1&3 \end{array}\right]$

A⁻¹ = adj A / | A|

$\left[\begin{array}{ccc}x \\y \end{array}\right] =-\dfrac{1}{22} \left[\begin{array}{ccc}-6&-4 \\-1&3 \end{array}\right] \left[\begin{array}{ccc}8 \\10 \end{array}\right]$

$\left[\begin{array}{ccc}x \\y \end{array}\right] =-\dfrac{1}{22} \left[\begin{array}{ccc}-88 \\22\end{array}\right]$

$\left[\begin{array}{ccc}x \\y \end{array}\right] = \left[\begin{array}{ccc}4 \\-1\end{array}\right]$

x = 4

y = - 1

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