Best Answer

This can happen in different ways:

a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc.

b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example:

y = 2x + 3

2y = 4x + 6

The second equation is simply the first equation multiplied by 2.

Study guides

☆☆

Q: A system of linear equations with an infinite number of solutions?

Write your answer...

Submit

Still have questions?

Continue Learning about Calculus

Any two numbers that make one of the equations true will make the other equation true.

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.

There are an infinite number of equations with this solution, eg x = 6 - 10; x = 45678 - 45682; x squared = 16 etc etc

It is not to solve so much as to see the number of solutions and whether there is a real solution to the equation. b2 - 4(a)(c) A positive answer = two real solutions. A negative answer = no real solution ( complex solution i ) If zero as the answer there is one real solution.

In this type of problem let the numerator of a fraction be 23.29 and its denominator be twice the coefficient of the variables and so:- 29*(23.29/58)+23*(23.29/46) = 23.29 Therefore the possible values of x and y are 23.29/58 and 23.29/46 respectively

Related questions

They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions

Any two numbers that make one of the equations true will make the other equation true.

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.

It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.

If the system is for more than two variables there will be an infinite number of solutions since only two of the variables can be determined while the rest will be free to take any value. Also, technically, it does not matter what the system is independent of. What matters is that the linear equations are independent of one another.

one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel

Infinite number of solutions

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.

Either an infinite number or none.

In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others

People also asked