How to tell how many solutions an equation has

How can you tell how many solutions an equation has without solving?

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur. Use distributive property on the right side first.

How do you know if an equation has more than one solution?

Summary. If the equation ends with a false statement (ex: 0=3) then you know that there’s no solution. If the equation ends with a true statement (ex: 2=2) then you know that there’s infinitely many solutions or all real numbers. Let’s see an example of both of these.

How do you know if an equation has two solutions?

YES, A SOLUTION IS JUST WHERE THE QUADRATIC CROSSES OVER THE X AXIS. Discriminant of a quadratic equation provides you with the indication of the number of solutions. For the equation ax2+bx+c=0, D=b2-4ac is the discriminant. 1) D>0; there are two distinct solutions.

What is an equation with no solution?

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. If you substitute these values into the original equation, you’ll see that they do not satisfy the equation.

What is a one solution equation?

You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

What equation has infinitely many solutions?

The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. Let’s see what happens when we solve it. We first combine our like terms.

Is 0 0 infinite or no solution?

For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other.

How do you know if a quadratic equation has infinite solutions?

In the quadratic formula, the only way to make it infinity would be if a = 0. Then the denominator would be zero, and hence the whole equation would be “infinity.” But if a = 0, then the equation is no longer quadratic, it is linear, right? For example, is the same as . That is just a line, it is linear, not quadratic.

How do you know if a quadratic equation has real solutions?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.A positive discriminant indicates that the quadratic has two distinct real number solutions.A discriminant of zero indicates that the quadratic has a repeated real number solution.

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How do you write an equation that has infinite solutions?

In this case, the idea is that you have to create something that makes both the right side of the equation and the left side to be equal to each other which gives you an infinite number of solutions. so if you have 5x-8 on the left, you need 5x-8 on the right for everything to cancel and end up with 0=0.

What if an equation is 0 0?

1 Expert Answer If the elimination produces the equation 0=0, then the two equations are for the same line. This means that there are an infinite number of solutions.

What are the 7 unsolved math problems?

Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000, six have yet to be solved as of July, 2020:P versus NP.Hodge conjecture.Riemann hypothesis.Yang–Mills existence and mass gap.Navier–Stokes existence and smoothness.Birch and Swinnerton-Dyer conjecture.

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