**Solving Equations by Matrix Method**

The simultaneous equations in two
variables can be solved by different methods: substitution method, cross
multiplication method etc. Here, we deal with the method of solving linear
equations of two variables using **matrices**.

Let us consider the following linear
equations,

a_{1}x + b_{1}y = c_{1}
………………. (i)

a_{2}x + b_{2}y = c_{2}
………………. (ii)

Writing equations (i) and (ii) in the
matrix form, we get

Equating the corresponding elements of equal
matrices X and A^{-1}B, we get the solution.

*Note:** If the determinant |A| = 0, the system of simultaneous equations have no unique
solution, therefore when |A| ≠ 0, the equations have unique solution.*

**Worked Out Examples**

*Example 3: If the cost of 17 kg sugar and 4 kg tea is Rs. 1110 and
the cost of 8 kg sugar and 2 kg tea is Rs. 540. Find the cost of sugar per kg and
tea per kg by matrix method.*

*Solution:** Let,*

*Cost of sugar per kg = Rs. x*

*Cost of tea per kg = Rs. y*

*Then according to questions,*

*1 ^{st} case, 17x + 4y = 1110 …………… (i)*

*2 ^{nd} case, 8x + 2y = 540 ……………… (ii)*

*Writing the given equations in the matrix form, we get*

*Comparing the corresponding elements, we get*

*x = 30, y = 150*

*Hence, The cost of
sugar per kg = Rs. 30*

* The cost of tea per
kg = Rs. 150*

*You can comment your questions or problems
regarding the solution of simultaneous equations by matrix method here.*

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