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What must be true about the lines of a system of equation that has not one solution but infinitely many solutions?
Wiki User
∙ 13y ago
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
Wiki User
∙ 13y ago
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What are the possible solutions for a system of equations?
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
A system of linear equation in two variables can have how many solutions?
None, one or an infinite number. In graph form, the three correspond to: None = Parallel lines One = Interscting lines Infinite = Coincident lines.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
What is the solution to this system of equations y equals -3x-2?
-1
Choose the ordered pair that is a solution to the system of equations -x plus y equals 12?
-x+y=12is the equation of a line and since there are infinitely many points on the line and each point is represented by an ordered pair, we have infinitely many solutions.If we take x as 0, then y must be 12so (0,12) is one ordered pair that is a solution to the equation.Zero is often a nice number to pick since it makes the calculation a bit easier.
How many solutions will a system have if the graph of the solution is not parallel lines?
infinitely many solutions :)
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
Can linear system that has more unknowns than equation be consistent?
yes it can . the system may have infinitely many solutions.
Can a linear system have exactly two solutions?
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
How many solutions does an inconsistent equation have?
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
When you use the substitution method how can you tell that a has an infinite number of solutions?
If the process of substituting leads to an identity rather than an equation then the system has infinitely many solutions.
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
Does this system of equation 5x - y equals 7 have one solution no solution or an infinite number of solutions?
-2
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
What does one solution mean in math?
An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)
How do you find the linear system if you know its solutions?
You cannot since there are infinitely many sets of lines that can pass through any single point - the solution.
What is the solution to a linear equation?
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
