Sometimes. Not always.
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 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.
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.
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).
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
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 coordinates of the point of intersection represents the solution to the linear equations.
A system of equations will have one solution if the graphs of the lines intersect. This is because the lines intersect at a single point. Let's say that point is (a, b). The x = a, y = b is the one and only solution for the system.
The solution is the coordinates of the point where the graphs of the equations intersect.
Parallel lines don't intersect, no matter how many of them there are.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
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.
It represents the point of intersection on a graph.
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.
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.
They are straight line graphs that work out the solutions of 2 equations or simultaneous equations
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).