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.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
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
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.
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.
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.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
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.
An infinite solution means that are an infinite number of values that are solutions.
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
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.
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
Infinite number of solutions
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.
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.