x=3
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 coordinates of the point of intersection represents the solution to the linear equations.
You see the point the two lines cross, if they do. This is the solution to the system since it is the values of (x,y) that are on both lines The solution is a sytems is those points, if any, (x,y) that satisfy both equations. That is the same as saying they are on both lines. If you graph the equations, this is the same as saying the points that are in the intersection of the lines. This is why parallel lines represent a system with no solution and if two equations are the same line there is an infinite number of solutions.
If the lines are straight lines , then there is only one solution, which is the point of intersection of the two lines. It will have ( x,y) coordinates. However, if the lines are curved in any way , there may be more than two or more points of intersection.
The system is inconsistent because there is no solution, i.e., no ordered pair, that satisfies both equations. You can see that this will be the case by seeing that their graphs have the same slope (2) but different y-intercepts (2 and 3/4 respectively). So the lines are parallel and will not intersect.
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.
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..
The two equations represent parallel lines.
A pair of simultaneous equations in two unknowns which are inconsistent - in the sense that there is no solution that simultaneously satisfies both equations. Graphically, the equations are those of two parallel lines (slope = 2). Since, by definition, they cannot meet there is no solution to the system.
They will be a set of lines meeting at one point - the solution.
perpendicular
8
The intersection of two lines in a graph of a system of linear equations represents the solution because it is the point where both equations are satisfied simultaneously. At this point, the x and y coordinates meet the conditions set by both equations, meaning that the values of x and y make both equations true. Hence, the intersection point is the unique solution to the system, assuming the lines are not parallel or coincident.