Question

solue by using matrix method
2x -3y=1 and 3x-y=3​

Answer 1

Answer:

Value of x = 8/7

Value of y = 3/7

Step-by-step explanation:

Given:

A pair of equations:

• 2x - 3y = 1
• 3x - y = 3

To Find:

• To solve the pair of equations by using matrix method

Solution:

Here,

$\sf A=\left[\begin{array}{cc}a_1&b_1\\a_2&b_2\end{array}\right]$

where a₁ = 2, a₂ = 3, b₁ = -3, b₂ = -1

$\sf B=\left[\begin{array}{c}c_1\\c_2\end{array}\right]$

where c₁ = 1, c₂ = 3

$\sf X=\left[\begin{array}{c}x\\y\end{array}\right]$

Substituting the data,

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

$\sf B=\left[\begin{array}{c}1\\3\end{array}\right]$

$\sf X=\left[\begin{array}{c}x\\y\end{array}\right]$

Now we know that,

X = A⁻¹B

Finding the inverse of matrix A,

$\sf A^{-1} =\dfrac{adj\:A}{|A|}$

$\sf A^{-1} =\dfrac{1}{7}\left[\begin{array}{cc}-1&3\\-3&2\end{array}\right]$

Multiplying it with matrix B,

$\sf X =\dfrac{1}{7}\left[\begin{array}{cc}-1&3\\-3&2\end{array}\right]\times \left[\begin{array}{c}1\\3\end{array}\right]$

$\sf X =\dfrac{1}{7}\left[\begin{array}{c}-1\times 1+3\times 3\\-3\times 1+2\times 3\end{array}\right]$

$\sf X =\dfrac{1}{7}\left[\begin{array}{c}8\\3\end{array}\right]$

$\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}8/7\\3/7\end{array}\right]$

Equating it we get,

x = 8/7

y = 3/7

Hence the value of x and y are 8/7 and 3/7 respectively.

Verification:

2 × 8/7 - 3 × 3/7 = 1

16/7 - 9/7 = 1

7/7 = 1

1 = 1

3 × 8/7 - 3/7 = 3

24/7 - 3/7 = 3

21/7 = 3

3 = 3

Hence verified.

Answer 2

Value of x = 8/7

Value of y = 3/7