The Total Amount Of Charge In Coulombs That Has Entered A Wire At Time Is Given By The Expression Q =
The systems that have no solution are A and C.
What is no solution ?
“No solution” is a term used in mathematics to describe a system of equations that has no solution or a solution that does not exist. It means that the equations are inconsistent and do not have a common solution that satisfies all of them simultaneously. Geometrically, this means that the corresponding lines, planes, or surfaces do not intersect in a single point in the coordinate space. When a system has no solution, it usually indicates that there is some error or contradiction in the problem statement or in the equations themselves.
The system that has no solution is the one that leads to a contradiction. This happens when the two equations are inconsistent and do not intersect in a single point in the coordinate plane. Geometrically, the lines corresponding to the equations are parallel and do not cross.To determine if a system has a solution, we can use different methods, such as substitution, elimination, or graphing.
For option A, we can use the elimination method by multiplying the first equation by 2 and adding it to the second equation, which gives:6x – 2y = 12-6x + 2y = 12————–0 = 24This leads to the equation 0 = 24, which is a contradiction. Therefore, the system has no solution.For option B, we can observe that the slopes of the two lines are different (-2 and 2), so they intersect in a single point.
Therefore, the system has a unique solution.For option C, we can divide the second equation by 2 to get y = 3x – 2. Substituting this expression into the first equation gives:3x – (3x – 2) = 12 = 1This leads to the equation 2 = 1, which is a contradiction. Therefore, the system has no solution.For option D, we can use the elimination method by multiplying the first equation by 3 and subtracting it from the second equation, which gives:-4x – 32 = -8Solving for x, we get x = 6. Substituting this value into the first equation gives y = 22.
Therefore, the system has a unique solution.Therefore, the systems that have no solution are A and C.
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