What should (t) not be for (3x+2y=11) and (6x+4y=t) to have no solution?
Answer and explanation
Correct answer: (22)
The first equation is 3x+2y=11. The second equation has coefficients 6 and 4, which are both twice the corresponding coefficients in the first equation. Therefore its left side is twice the first left side. If the equations represented the same line, its right side would also have to be twice 11, namely 22.
Thus t=22 makes the second equation 2(3x+2y)=22, exactly the same equation, giving infinitely many solutions. For every other listed value, the coefficient ratios remain equal but the constant ratio is different, so the lines are distinct and parallel and there is no solution. Therefore t must not be 22, and option C is correct.
Frequently asked questions
What is the correct answer to this question?
(22)
Why is this the correct answer?
The first equation is 3x+2y=11. The second equation has coefficients 6 and 4, which are both twice the corresponding coefficients in the first equation. Therefore its left side is twice the first left side. If the equations represented the same line, its right side would also have to be twice 11, namely 22.
Thus t=22 makes the second equation 2(3x+2y)=22, exactly the same equation, giving infinitely many solutions. For every other listed value, the coefficient ratios remain equal but the constant ratio is different, so the lines are distinct and parallel and there is no solution. Therefore t must not be 22, and option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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