# Write a system of equations that can be solved by elimination

Now we want to solve for our y value.

And 4 Fruit Roll-Ups. If I subtract 3x plus y, that is the same thing as negative 3x minus y, if you just distribute the negative sign. In this situation, they would end up being the same line, so any solution that would work in one equation is going to work in the other.

## System of equations calculator

This would be the coordinate of their intersection. So you divide both sides. Is there something we could add to both sides of this equation that'll help us eliminate one of the variables? You could solve this using any of the techniques we've seen so far-- substitution, elimination, even graphing, although it's kind of hard to eyeball things with the graphing. What I want is to introduce a multiplier to one of the equations, or both, and then observe if I arrive at some coefficients that only differ in signs. Multiplying the entire equation by any nonzero number does not change its original meaning. Because D is equal to D, so I won't be changing the equation. You get 4x minus-- sorry, 4y minus y. Now we can substitute back into either of these equations to figure out the cost of a candy bar.

They're going to be plus 0y. I'm just taking the second equation. The process or procedure of solving for y should be similar below. If you said inconsistent, you are right!

What I want is to introduce a multiplier to one of the equations, or both, and then observe if I arrive at some coefficients that only differ in signs.

The graph below verifies that our solution is correct.

## Elimination method examples

This is easy to find since I already know what x is. You can create one equation from the other by just multiplying through by a constant. Graphically, the solution looks like this. This is quite interesting because no variables will cancel when added. Practice with Worksheets. All right. That's equivalent to-- let's see, this is Solve the simple equation that arises from it. Bring down a 0. And that's going to be equal to 2. His interests include development economics, technology-based charities, and angel investing. You should see that the plan works since adding the x-column results to the cancellation of x. Because D is equal to D, so I won't be changing the equation.

If you get no solution for your final answer, would the equations be dependent or independent? You could do it with the bottom one as well.

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