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The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
- a)Unique solution
- b)Exactly two solutions
- c)Infinitely many solutions
- d)No solution
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)U...
9x + 3y + 12 = 0 and 18x + 6y + 26 = 0
So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.
Hence, the correct option is (D).
Most Upvoted Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)U...
Solution:
Given,
9x - 3y + 12 = 0 …(1)
18x - 6y + 26 = 0 …(2)
To check the consistency of the system, we can use any of the following methods:
Method 1: Using determinants
We can write the given equations in matrix form as:
$\begin{bmatrix}9 & -3\\ 18 & -6\end{bmatrix}$ $\begin{bmatrix}x \\ y\end{bmatrix}$ = $\begin{bmatrix}-12 \\ -26\end{bmatrix}$
Now, for the given system of equations to be consistent, the determinant of the coefficient matrix should be equal to zero.
i.e., $\begin{vmatrix}9 & -3\\ 18 & -6\end{vmatrix} = 0$
Simplifying the determinant gives:
$\begin{vmatrix}9 & -3\\ 18 & -6\end{vmatrix}$ = (9 x (-6)) - (-3 x 18) = -54 + 54 = 0
Since the determinant of the coefficient matrix is zero, the system of equations may have infinitely many solutions or no solution.
Method 2: Using algebraic manipulations
We can rewrite the given equations as:
3(3x - y + 4) = 0 …(1')
6(3x - y + 4) = -4 …(2')
Equation (1') implies that 3x - y + 4 = 0 or y = 3x + 4
Substituting this value of y in equation (2'), we get:
6(3x - (3x + 4) + 4) = -4
Simplifying the above equation gives:
6(4) = -4
24 = -4
This is a contradiction. Hence, the given system of equations has no solution.
Therefore, the correct answer is option (D) - No solution.
Given,
9x - 3y + 12 = 0 …(1)
18x - 6y + 26 = 0 …(2)
To check the consistency of the system, we can use any of the following methods:
Method 1: Using determinants
We can write the given equations in matrix form as:
$\begin{bmatrix}9 & -3\\ 18 & -6\end{bmatrix}$ $\begin{bmatrix}x \\ y\end{bmatrix}$ = $\begin{bmatrix}-12 \\ -26\end{bmatrix}$
Now, for the given system of equations to be consistent, the determinant of the coefficient matrix should be equal to zero.
i.e., $\begin{vmatrix}9 & -3\\ 18 & -6\end{vmatrix} = 0$
Simplifying the determinant gives:
$\begin{vmatrix}9 & -3\\ 18 & -6\end{vmatrix}$ = (9 x (-6)) - (-3 x 18) = -54 + 54 = 0
Since the determinant of the coefficient matrix is zero, the system of equations may have infinitely many solutions or no solution.
Method 2: Using algebraic manipulations
We can rewrite the given equations as:
3(3x - y + 4) = 0 …(1')
6(3x - y + 4) = -4 …(2')
Equation (1') implies that 3x - y + 4 = 0 or y = 3x + 4
Substituting this value of y in equation (2'), we get:
6(3x - (3x + 4) + 4) = -4
Simplifying the above equation gives:
6(4) = -4
24 = -4
This is a contradiction. Hence, the given system of equations has no solution.
Therefore, the correct answer is option (D) - No solution.
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Community Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)U...
9x + 3y + 12 = 0 and 18x + 6y + 26 = 0
So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.
Hence, the correct option is (D).
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The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)Unique solutionb)Exactly two solutionsc)Infinitely many solutionsd)No solutionCorrect answer is option 'D'. Can you explain this answer?
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