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Q: The equations of two lines are 6x-y equals 4 and y equals 4x plus 2. What is the value of x in the solution for this system of equations?

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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.

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.

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.

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.

Related questions

If a system has no solution, it means that the lines are parallel.

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

extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.

The two equations represent parallel lines.

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.

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..

They will be a set of lines meeting at one point - the solution.

perpendicular

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.

The coordinates of the point of intersection represents the solution to the linear equations.

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