Write a system of equations that has infinitely many solutions

There will not be a solution.

Gaussian Elimination

And of course, we still have our minus 8. The three types of solution sets: There are still only these three possibilities. GO Consistent and Inconsistent Systems of Equations All the systems of equations that we have seen in this section so far have had unique solutions.

This happens when as we attempt to solve the system we end up an equation that makes no sense mathematically. For example, solve the system of equations below: Gaussian elimination is usually carried out using matrices. This is a contradiction, and so the system has no solutions.

Fact Given any system of equations there are exactly three possibilities for the solution.

MA 162: Finite Mathematics

Well, if we make this a minus 8, or if we subtract 8 here, or if we make this a negative 8, this is going to be true for any x.

Adding row 2 to row 1: So we will get negative 7x plus 3 is equal to negative 7x. Solve the following system using Gaussian elimination: For example; solve the system of equations below: Determine all solutions of the system Write down the augmented matrix and perform the following sequence of operations: And you probably see where this is going.

First, if we have a row in which all the entries except for the very last one are zeroes and the last entry is NOT zero then we can stop and the system will have no solution. And so 4x plus x is 5x. If I just get something, that something is equal to itself, which is just going to be true no matter what x you pick, any x you pick, this would be true for.

Theorem C, which concerns a linear system, has a counterpart in the theory of linear diffrential equations. Zero is always going to be equal to zero. When these planes are parallel to each other, then the system of equations that they form has infinitely many solutions.

Now if you go and you try to manipulate these equations in completely legitimate ways, but you end up with something crazy like 3 equals 5, then you have no solutions.

This means that we can pick any value of x or y then substitute it into any one of the two equations and then solve for the other variable. All three planes have to parallel Any two of the planes have to be parallel and the third must meet one of the planes at some point and the other at another point.

But if you could actually solve for a specific x, then you have one solution. In this system it is -2 and in the previous example it was Two lines are parallel if they have the same slope. When two lines are parallel, their equations can usually be expressed as multiples of each other and that's usually a quick way to spot systems with infinitely many solutions.

And if you add 7x to the right hand side, this is going to go away and you're just going to be left with a 2 there. So in this scenario right over here, we have no solutions.

First, if we have a row in which all the entries except for the very last one are zeroes and the last entry is NOT zero then we can stop and the system will have no solution. And actually let me just not use 5, just to make sure that you don't think it's only for 5.

Consistent and Inconsistent Systems of Equations

But not only do they have the same slope, they are actually the same line, and so the two lines intersect in infinitely many points.

The only difference is the number to the right of the equal sign in the second equation. Recall that we still need to do a little work to get the solution.

Number of solutions to equations

I'll add this 2x and this negative 9x right over there. This example will also illustrate an interesting idea about systems.A system of equations that has infinitely many solutions.

x + y = 2 2x + 2 y = 4. a solution to a system of equations in 3 variables written in the following form: (x, y, z) Unit 5 - Systems of Equations and Inequalities. 43 terms. System of Linear Equations - Unit 4. A system of linear equations can have no solution, a unique solution or infinitely many solutions.

A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution.

Systems of Linear Equations

So this system has infinitely many solutions, as the equations both correspond to the same line and lines have infinitely many points. (Bonus) In parts (a), (c), and (d), there are infinitely many equations that can be found. Jan 21,  · Write a system of equations that has infinitely many solutions, and explain why?

I have a take home algebra test and I need to get a % I really need help. That's all the information the question gave kaleiseminari.com: Resolved.

Systems of Linear Equations

A System of Linear Equations is when we have two or more linear equations working together. Systems of Linear Equations: No solutions and infinitely many solutions Example 1: A system with no solutions Consider the system of equations \[ \begin{cases} \begin{array}{ccccc} 3x & - & 2y & = & 3 \\ 6x & + & k\cdot y & = & 4 \\ \end{array} \end{cases} \] Find .

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Write a system of equations that has infinitely many solutions
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