If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has
infinitely many solutions
.
How do you know how many solutions a system of equations has?
A system of two equations can be classified as follows:
If the slopes are the same but the y-intercepts are different
, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
How can you tell how many solutions an equation has without solving?
Correct answer:
The
coefficients
are the numbers alongside the variables. 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.
How many solutions does a equations have?
A system of linear equations usually has
a single solution
, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.
How do you know how many solutions a quadratic equation has?
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.
How do you know if an equation has infinitely many solutions?
We can identify which case it is by looking at our results.
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x
, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
How do you know if a system has no solution?
If a system has no solution, it is said to
be inconsistent
. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
How many solutions are there?
There
can be zero solutions
, 1 solution or infinite solutions–each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case–a stem with exactly 2 lines.
How do you tell if a quadratic equation has a solution?
- If you get a positive number, the quadratic will have two unique solutions.
- If you get 0, the quadratic will have exactly one solution, a double root.
How do you know if a quadratic equation has real solutions?
If the discriminant is greater than 0, the quadratic equation has 2 real solutions.
If the discriminant is equal to 0, the quadratic equation
has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions.
What does infinite solutions look like?
When a problem has infinite solutions, you’ll end up with a statement that’s
true no matter what
. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. … This means no matter what number you put in for the variable x, you will always get a number equaling itself.
How do you know if a solution is infinite?
Well, there is a simple way to know if your solution is an infinite solution.
An infinite solution has both sides equal
. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.
How can you tell how many solutions a discriminant has?
It tells you the number of solutions to a quadratic equation.
If the discriminant is greater than zero, there are two solutions
. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.
How many solutions does the first equations have?
An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has
infinitely many solutions
. The lines are exactly the same, so every coordinate pair on the line is a solution to both equations.
What does find all solutions mean?
According to this definition, if y=f(x), then finding the coordinates of x that make y=0 means finding the values that make the following equation true: y=0. The solution to several simultaneous equations, called a system of equations, are the values that make all equations
true
at the same time.
What is a one solution equation?
To create a one solution equation, we can honestly create an
equation
using any number we want as long as we don’t have the same amount of variables on both sides of the equation.
How many solutions does the system of equations above have?
The system of equations above has how many solutions? One approach is to begin solving the system (using the elimination method) and see what happens. As we can see, this equation has
infinitely many solutions
.
How many solutions exist for the system of equations in the graph?
Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is
one solution
that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
How many solutions does X Y 5 have?
Use the x x and y y values to form the ordered pair. These are
three possible solutions
to the equation.
How many solutions does a dependent system of equations have?
A dependent system of equations has
infinite solutions
, and an independent system has a single solution.
What equation has two solutions?
A quadratic equation
has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
How do we know that the solutions are two complex conjugate imaginary solutions?
they always occur in conjugate pairs. Imaginary or complex roots will occur
when the value under the radical portion of the quadratic formula is negative
. … It quickly tells you if the equation has two real roots (b
2
– 4ac > 0), one real repeated root (b
2
– 4ac = 0) or two complex conjugate roots (b
2
– 4ac < 0).
