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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.
How the solution of a linear system with two equations is represented by the point where the graphs of the two equation intersect?
The first graph consists of all points whose coordinates satisfy the first equation.The second graph consists of all points whose coordinates satisfy the second equation.The point of intersection lies on both lines so the coordinates of that poin must satisfy both equations.
What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
What is the situation when two linear inequalities have no common solution?
To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).
Does a graph of a system of equations intersect more than 1 point?
In some special cases lines can end up intersecting each other at every point, which means the two seperate lines are on top of each other, where you end up having infinite solutions
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.
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.
The solution to a two-variable system is the point on a graph at which the lines cross?
Yes, the solution to a two-variable system is the point where the equations of the lines representing the system intersect on a graph. This point represents the values of the variables that satisfy both equations simultaneously.
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.
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.
Solving the system of equations by graphing?
Solving a system of equations by graphing involves plotting the equations on the same coordinate plane and finding the point(s) where the graphs intersect, which represents the solution(s) to the system. Each equation corresponds to a line on the graph, and the intersection point(s) are where the x and y values satisfy both equations simultaneously. This method is visually intuitive but may not always provide precise solutions, especially when dealing with non-linear equations or when the intersection point is not easily identifiable due to the scale or nature of the graphs.
Will the graph of a system of parallel lines intersect at exactly 1 point?
Parallel lines don't intersect, no matter how many of them there are.
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.
How the solution of a linear system with two equations is represented by the point where the graphs of the two equation intersect?
The first graph consists of all points whose coordinates satisfy the first equation.The second graph consists of all points whose coordinates satisfy the second equation.The point of intersection lies on both lines so the coordinates of that poin must satisfy both equations.
What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
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.
