# Write a system of equations with no solution

To distinguish chemical changes from physical changes. To write chemical equations to describe a chemical reaction. Solving linear systems with three variables Video transcript Determine whether the system has no solutions or infinite solutions. So let's think about how we can go about doing this. So if at any point we might not have to solve this entirely if we somehow get something that's nonsensical which will tells us there's no solutions.

Or we might have to go further and see if it's one or infinite solutions, although it looks like one solution isn't an option here, given how this question is phrased. So the way that you would proceed to solve three equations with three unknowns is you would try to eliminate variables one by one.

And so first we could try to eliminate the x variables. And we could do that, we can essentially create two equations with two unknowns. The two unknowns will be y and z.

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If we can pair up these equations and eliminate x with each of these pairings. So for example, we can pair these first two. We can pair the last two. And that's all we would need to have to eliminate the x's and still have two equations. And have all of the information of these three equations. But then the third pairing would be the first and the third equation, But we only have to do two of these pairings. Now, just to show you what I mean by these pairings, what I want to do is take these first two.

I'm going to pair this first pairing right over here, and I'm going to use them to eliminate the x terms. And over here I have 2x, over here I have 8x.

If I could turn this 2x into a negative 8x I could add both sides of these equations to each other and the x terms would cancel out. And so the best way to turn this 2x into a negative 8x is to multiply this top equation times negative 4.

When I say multiply, I'm saying multiply the whole equation, both sides of it, by negative 4. So 2x times negative 4 is negative 8x. Negative 4y times negative 4 is plus 16y, are positive 16y.

And then I can rewrite this equation right over here. It's 8x minus 2y plus 4z is equal to 7. And now I can add these both equations. On the left hand side, these guys cancel out, 16y minus 2y-- and that was the whole point behind multiplying the top equation by negative 16y minus 2y is 14y.

Negative 4z plus 4z. These guys actually cancel out as well. So actually with that one pairing, by multiplying by negative 4 we were actually able to cancel out two variables. So you get 14y is equal to negative 12 plus 7 is equal to negative 5. And you can actually solve for y. And we don't know if this one will actually have solutions.

But if we assume it's going to have a solution, you could actually solve for y right over here.How to Balance Chemical Equations. In this Article: Article Summary Traditional Balance Algebraic Balance Community Q&A A chemical equation is a written symbolic representation of a chemical reaction.

The reactant chemical(s) are given on the left-hand . Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. Section Solving Exponential Equations. Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them.

Mathematics Enhanced Scope and Sequence – Algebra II Virginia Department of Education © 2 algebraically and Partner B to solve the same problem graphically. 70 2 SYSTEMS OF LINEAR EQUATIONS AND MATRICES system. Geometrically, the two equations in the system represent the same line, and all solutions of the system .

With this direction, you are being asked to write a system of equations. You want to write two equations that pertain to this problem.

Notice that you are given two different pieces of information. You are given information about the price of the shoes and the number of shoes bought. Therefore, we will write one equation for both pieces of information.

Writing a System of Equations