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A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution.

With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.

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Q: Can a system of linear equation have more than one solutions?

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No. The graph of each linear equation is a straight line, and two or more lines can't all intersect at more than one point. * * * * * Unless all the lines are, in fact, the same line. In that case each point on the line is a solution. That is, there are infinitely many solutions.

The statement "A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line" is true.

Simultaneous equation

A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.

In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

Related questions

yes it can . the system may have infinitely many solutions.

The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.

A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.

No. The graph of each linear equation is a straight line, and two or more lines can't all intersect at more than one point. * * * * * Unless all the lines are, in fact, the same line. In that case each point on the line is a solution. That is, there are infinitely many solutions.

we study linear equation in other to know more about quadratic equation

A "system of equations" implies that there is more than one equation.

The statement "A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line" is true.

Simultaneous equation is nothing: it cannot exist.A system of simultaneous equations is a set of 2 or more equations with a number of variables. A solution to the system is a set of values for the variables such that when the variables are replaced by these values, each one of the equations is true.The equations may be linear or of any mathematical form. There may by none, one or more - including infinitely many - solutions to a system of simultaneous equations.

A linear equation in n-dimensional space is of the form a1x1 + a2x2 + ... + anxn + c = 0 where the ai are numerical constants and the xi are variables. The equation represents a straight line in n-dimensional space. A non-linear equation is one in which one or more of the xi have a power other than 1. The equation will represent a curve. A linear system is one in which you will get the same result if you change an input by the same amount - from whatever starting level. Otherwise the system is non-linear.

A linear can't have more than one solution. WRONG!A linear system can have more than 1 solution. It can also have no solution.Example: x+y=1z+y=2This system has infinitely many solutions. Y can equal anything and x and z can then be determined.Example: x+y=1y=1x=5This system obviously has no solution because if x=5 and y=1, then x+y can never equal 1.

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.

No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2

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