The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsistentb)Bothc)consistentd)none of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

a₁ / a₂ = b₁ / b₂ = c₁ / c₂
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a₁ / a₂ = b₁ / b₂ = c₁ / c₂
When these are equal then it is consistent.
Therefore option (C) is correct .

Answer

Answer

A1 / a2 = b1 / b2 = c1 / c2
2 / 4 = 3/ 6 = 5 / 10
1 / 2 = 1/ 2 = 1 / 2
So a1 / a2 = b1 / b2 = c1 / c2 ( infinitely many solutions )
When ^ these are qual then it is consistent.
Therefore option (C) is correct .

Answer

A1 / a2 = b1 / b2 = c1 / c2
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2
When these are equal then it is consistent.
Therefore option (C) is correct .

Answer

On multiplying the first equation with we are getting the second one. So, any value of x and y satisfy these equations or to say there are infinite solutions. By consistent equations we mean that there exists at least one pair of X and y which satisfies both the equations. Hence the given equations are consistent.

There's another way to check whether the given equations are consistent are not. The determinant of the matrix formed by taking the co-efficients of x and y from both the equations must be zero.The matrix in this case is M = [2 3][4 6] and it's determinant is D = 2(6) - 4(3) = 0 and hence the equations are consistent. Also, if there are 3 equations with 3 unknown you can do it by a 3 x 3 matrix.

Answer

Given pair of linear equations are:

2x + 3y = 5 --------(1)

4x + 6y = 10 ------(2)

To check whether these equations are consistent or not, we need to find the value of x and y that satisfies both equations.

Dividing equation (2) by 2, we get:

2x + 3y = 5 ------(1)

2x + 3y = 5 ------(2)

Both equations are the same. This means that these equations represent the same line.

Therefore, the given pair of linear equations have infinitely many solutions, and hence, are consistent.

Hence, option (C) is the correct answer.

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