Question

Find whether the following pair of linear equation has a unique solution or not. If yes, find the solution. 7x-4y=49,5x-6y=57 Please find this

Answer 1

ans of the ques is

x=3

y=-7

Answer 2

The solution is (3,-7) .

Explanation:

The given system of linear equations :

$7x-4y=49$                  (1)

$5x-6y=57$                   (2)

Since the ratio of the coefficient of x term is not equal to the ratio of coefficient of y term , so this system has unique solution.

Multiply the equation (1) by 3 and equation (2) by 2 , we get

$21x-12y=147$     (3)

$10x-12y=114$        (4)

Eliminate (4) from (3) , we get

$11x=33\\\\\Rightarrow\ x=3$

Put value of x in (1) , we get

$7(3)-4y=49\\\\ -4y=49-21=28\\\\\Rightarrow\ y=-7$

Hence, the solution is (3,-7).

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What is the minimum number of solution that a system of simultaneous linear equation must have, if it is a consistent system

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