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The graph of a system of equations with the same slope will have no solutions?
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
What is the consistent equation in mathematics?
Consistent equations are two or more equations that have the same solution.
What is a system of equations that has at least one solution?
a linear equation
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
The graph of a system of equations with the same slope will have no solutions?
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
When solving a system of equations by graphing how is the solution found?
The solution is the coordinates of the point where the graphs of the equations intersect.
How many solutions can two lines have that intersect once?
Since the lines that intersect are the equations, if they intersect once they have one solution.
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.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
What is the point at which the lines intersect in a system of linear equations?
The coordinates of the point of intersection represents the solution to the linear equations.
The solution of a system of equation is?
the solution to a system is where the two lines intersect upon a graph.
Can 0 be the solution of an equation?
Yes, zero can and is the solution of many equations.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
