4 Useful Tips for Solving Systems of Equations by Elimination
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Here’s How to Solve Systems of Equations by Elimination
Solving Systems of Equations by Elimination is a method to solve a system of two linear equations. Solving Systems of Equations by Elimination follows a specific process in order to simplify the solutions. The first thing you must do when Solving Systems of Equations by Elimination is to multiply either equation so that when you add them vertically, one of the variables will cancel out. Next, you must add the equations together vertically to cancel out one variable. Then you solve for the variable that was not cancelled out. Use the solution of the variable to substitute back in to either original equation. The last step when Solving Systems of Equations by Elimination is to solve for the last variable by following order of operations.
Common Core Standard: 8.EE.C
Related Topics: Identifying One, None, Infinite Solutions, Solving Systems by Graphing, Solving Systems by Substitution
A Short Guide for Completing any Elimination Method Example Problem
Here’s how to learn how to solve system of equations by elimination: Solving Systems of Equations by Elimination is a technique to explain an arrangement of two mathematical statements. The first thing you should do when Solving Systems of Equations by Elimination is to change either mathematical statement with the idea that they will cancel when you add them together. Next, you should add the equations together vertically to eliminate one variable. At that point you simplify for the variable that was not eliminated. Use the answer for the variable to substitute back in to either mathematical statement. The last part for how to do elimination is to simplify for the last variable by using order of operations.
6 Quick Steps for Solving Systems of Equations by Elimination
- Multiple one, or both, equations so that when you add them together one variable will cancel.
- After you have multiplied, add the equations together.
- Solve for the variable that was left over after the other one was cancelled out.
- Substitute your solution for the first variable back into either equation.
- Solve for the second variable.
- Your answer must be in an x and y coordinate.
Systems of Equations Elimination Method Practice Problems Quiz
Watch the video where we complete our Elimination Method Worksheet
Watch our free video on how to solve Systems of Equations by Elimination. This video shows how to solve problems that are on our free Solving Systems by Elimination worksheet that you can get by submitting your email above.
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This video on solving systems of equations by elimination. You can get the solving systems of equations worksheet used in this video for free by clicking on the link in the description below.
Here’s number one on our solving systems of equations by elimination worksheet. This problem gives us two separate equations in our system. The first equation is 3x minus y equals 7 and the second equation is negative 2x plus y equals 2. When you do the elimination method to solve systems of equations you’re going to add each part of your equation vertically so that one or more of the terms will cancel. In the case of solving systems by using the elimination method you have to visualize how you couldn’t add these vertically to see what terms or variables will cancel. Now it does not matter if you cancel out the X or the Y but at least one of them must cancel.
We can look at our equations and we can see that if we were to add these straight down the Y’s would cancel so what would happen is you would do 3x plus negative 2x would be 1x or 3x minus 2x would be 1x and then negative y plus 1y. This is negative 1 y plus 1 Y would be 0 Y and then 7 plus 2 is 9. In other words what has happened is we have taken Y because we have 0y now and we have canceled it out. It is now gone and we are left with 1x or just x equals 9. Now we know that x equals 9 we can take x equals 9 and we can substitute x equals 9 back into one of our equations. The elimination method is just one way to figure out how to solve a system of equations but this is the easiest way to learn how to do elimination.
In this case we’re going to take this 9 and we’re going to substitute it in back into our first equation. This 9 because X is equal to 9 can get substituted in for X. Now we have 3 times 9 which is what we substituted in 4 minus y equals 7. So now we know X is equal to nine but we have to find y because we have to know the X and the y coordinate for this solution of this system we took our X which was nine and we substituted in for X then we’re going to simplify this. 3 times 9 is 27 minus y equals 7. Then we have to solve for y. We’re going to go ahead and subtract 27 from this side subtract 27 from this side these cancel you have negative y equals 7 minus 27 is negative 20 and then we have to get rid of this negative. We divide both sides by negative 1, these cancel and you have positive y equals positive 20. We know our x coordinate and we know our Y is now 20. We know that our solution is the coordinate 9, 20 and that’s going to be our answer.
The next problem on our solving system of equations by elimination worksheet is number two. We have to first know how to solve by elimination. X plus y equals 4 and then 2x minus 3y equals 18. When we go to eliminate these you will notice that if we were to add these straight up or down nothing would cancel. If we added these right now for instance X plus 2 X would be 3 X and then Y minus 3 y would be negative 2y and then 4 plus 18 would be 22. Nothing cancelled so that means we can’t do this, we have to multiply one or both equations so that we get a situation where when we add vertically something will cancel.
Our first equation can be multiplied that when we add these they will cancel now the easiest thing to multiply the top equation by would be 3 because if we multiplied everything by 3 we would get 3y and then the Y’s would cancel. The positive 3y and the negative 3y would cancel when we add we could also multiply by negative two because if we multiply by negative two we could add the x’s and that negative two and the positive 2x would cancel. Tou can pick and choose if you want to do X or if you want to cancel Y but in this case I’m going to cancel Y.
What we’re going to do is we’re going to go ahead and multiply the top equation by three so that we will get positive 3y and then this times three we’re multiplying everything times three. We have to distribute this three to both the X and the y on this side. We’re going to say 3 times X is 3x and then three times y is 3y and then is equal to 4 times 3 which is 12. Then our second equation we don’t have to change because we know that this positive 3y and this negative 3y are going to cancel. We’re just going to rewrite the second equation over here as 2x minus 3y equals 18. Then what we’re going to do is we’re going to add vertically. We will add both equations together because we know that the Y’s are going to cancel. 3x plus 2x is 5x and then 3y plus negative three Y would be 0y or the Y’s would just cancel. And then 12 plus 18 is 30 now the 0y has gone. We’ll just cancel it like that. We’ve got 5x equals 30 now. Then in order to solve for X we’re going to divide both sides by 5. These cancel and then 30 divided by 5 is 6.
Now we know x equals 6 we’re going to take x equals 6 and we’re going to substitute it back into either equation. In the case of this system it is easiest to substitute the 6 in or the first equation because our first equation is just X plus y equals 4 and this does not have a coefficient. We will rewrite our equation. We have X which is 6 so we substituted six in for X plus y equals four. Then we have to solve for y. We’ll subtract six from both sides, these cancel and we get y equals negative two. Our solution is x equals six y equals negative two and that’s the answer. Try the practice problems by downloading the free solving system of equations by elimination worksheet above.
Solving Systems of Equations by Elimination
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