Math and Arithmetic
Algebra

# What type of system equation produces the solution set infinite solution?

If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example,

3x + 2y = 8

6x + 4y = 16

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## Related Questions

Any equation, such as yours, with two variables (x and y, on your case) has an infinite number of solutions.

The equation or a system of equations having infinite solutions is called identity/identities. (a+b)^2=a^2+2ab+b^2 is an identity. It has infinite solutions. The equation is true for all values of a and b.

Ordered Pair * * * * * An ordered SET. There can be only one, or even an infinite number of variables in a linear system.

the solution to a system is where the two lines intersect upon a graph.

An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)

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

say system of equation is as follows a1x + b1y = c1 a2x + b2y = c2 if a1/a2 = b1/b2 = c1/c2 equation will have infinite answers

x - 2y = -6 x - 2y = 2 subtract the 2nd equation from the 1st equation 0 = -8 false Therefore, the system of the equations has no solution.

It is a system of linear equations which does not have a solution.

No, if two lines are parallel they will not have a solution.

No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.

If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.

A dependent system is defined as "a system of equations that has infinite solutions." It is an equation that is used in various mathematical situations.

Nothing yet. It only means that the equations you have are not independent ...one of them is a simple multiple of another one. All you can say so far is thatyou need another equation.

The given terms do not include an equality sign and as such it can't be considered to be an equation so therefore it has no solutions.

It depends on the equation. It could have one, it could have an infinite number.

Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.

Two lines with the same slope and y-intercept look like one single line. The "system" of equations consists of the same equation twice. The lines coincide at every point, which means there are an infinite number of solutions.

The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.

Without a second independent equation, it's not a 'system' yet.

If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.

When the two equations actually represent the same line, the solution to the system will be all points on the line. For example take the line y=x+2, if we multiply both sides of the equation by 2 we do not change anything about the line. So the equation 2y=2x+4 is really the same equation. The solution to the system y=x+2 and 2y=2x+4 is all the points ( all the real numbers) on the line. We often write this {(x,y)|y=x+2}

Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.

The solution to a system is an ordered pair (x,y) where the two lines intersect.