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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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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

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

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.

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.

A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.

The values for which the equations are solved. Graphically the intersection of the lines that are the solutions to the individual equations. The link below gives some explanations. The equations themselves will have to be given for a solution to be found.

For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.

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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).

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 pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.

Then they are simultaneous 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.

There is no solution for those equations because the lines are parallel so, they never touch.

There are two equations in the question, not one. They are the equations of intersected lines, and their point of intersection is their common solution.

They are two equations in two unknown variables (x and y), which are inconsistent. That is to say, there is no simultaneous solution. An alternative approach is to say that they are the equations of two lines in the Cartesian plane. The lines are parallel and so they do not meet indicating that there is no simultaneous solution.