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Q: Can a system of two quadratic equations have two solutions?

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A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.

A.infinitely manyB.oneD.zero

A quadratic equation can have either two real solutions or no real solutions.

None, one or infinitely many.

No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).

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Quadratic curves only have two solutions when the discrimant is greater than or equal to zero.

If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.

Yes and sometimes the two solutions are equal

A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.

If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.

Yes, a system can, in fact, have exactly two solutions.

No. A quadratic may have two identical real solutions, two different real solutions, ortwo conjugate complex solutions (including pure imaginary).It can't have one real and one complex or imaginary solution.

In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

False. There can either be zero, one, or infinite solutions to a system of two linear equations.

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

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