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When the two equations actually represent the same line, the solution to the system will be all points on the line.
For example take the line y=x+2, if we multiply both sides of the equation by 2 we do not change anything about the line. So the equation 2y=2x+4 is really the same equation. The solution to the system y=x+2 and 2y=2x+4 is all the points ( all the real numbers) on the line. We often write this {(x,y)|y=x+2}
What else can I help you with?
There is a system of linear equations with exactly two solutions is it true or false?
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
If a system has many solutions what kind of system of equations is it?
Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.
It is possible for a system of linear equations to have an infinite number of solutions.?
Yes, a system of linear equations can have an infinite number of solutions when the equations represent the same line or when they are dependent on each other. This typically occurs in systems with fewer independent equations than variables, leading to free variables that allow for multiple solutions. In such cases, the solutions can be expressed in terms of parameters, indicating a whole line or plane of solutions rather than a single point.
What is a system of linear equations in two variables?
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
There is a system of linear equations with exactly two solutions is it true or false?
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
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.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
If a system of equations is dependent how many solutions will it have?
Infinite simultaneous solutions. (The two equations represent the same line) OR If your in nova net the answer should be ( Many )
If a system has many solutions what kind of system of equations is it?
Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.
What is a dependent system?
A dependent system is defined as "a system of equations that has infinite solutions." It is an equation that is used in various mathematical situations.
What is system dependability?
A dependent system is defined as "a system of equations that has infinite solutions." It is an equation that is used in various mathematical situations.
How many solutions does a system of equations have?
It depends on the equation. It could have one, it could have an infinite number.
What is infinite solutions?
The equation or a system of equations having infinite solutions is called identity/identities. (a+b)^2=a^2+2ab+b^2 is an identity. It has infinite solutions. The equation is true for all values of a and b.
It is possible for a system of linear equations to have an infinite number of solutions.?
Yes, a system of linear equations can have an infinite number of solutions when the equations represent the same line or when they are dependent on each other. This typically occurs in systems with fewer independent equations than variables, leading to free variables that allow for multiple solutions. In such cases, the solutions can be expressed in terms of parameters, indicating a whole line or plane of solutions rather than a single point.
What is a system of linear equations in two variables?
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
Can a system of two linear equations in two variables have 3 solutions?
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions
