Now, you need some practice.
1. Solve using elimination:
The system is ready for elimination as it is. If we add both equations, the 2y and the -2y form a zero pair and are eliminated from the resulting equation.
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Add the two equations, then divide both sides of the equation by 7. |
Find the value of y by substituting 2 in for x in one of the original equations. I chose the first equation because every term was positive.
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Replace x with 2 |
Check the accuracy of your point by substituting in both 2 and 5 into the 2nd equation—the equation that we did not use to find y.
Since -2 is what we were supposed to get, we did the work correctly.
The solution to the system is (2, 5).
2. Solve using elimination :
The system needs to be prepared for elimination because just adding the two equations right now would not eliminate a variable. You first want to look through the equation to see if any of the coefficients for the variables is 1. Since x in the first equation fits this request, x is the variable that we will eliminate.
We will need to multiply the first equation by -3. Why? To make a zero pair, the coefficients for the variable must be the same number but with opposite signs. Since the coefficient of x in the second equation is 3, we need to change the coefficient of x in the first equation to -3 (its opposite). We make this change through multiplication.
Find the value of x by substituting 3 in for y in one of the original equations. I chose the second equation because of the smaller numbers
Check the accuracy of your point by substituting in both -5 and 3 into the first equation—the equation that we did not use to find x.
(-5) – 4(3) =
-5 – 12 = -17 Since -17 is what we were supposed to get, we did the work correctly.
The solution to the system is (-5, 3).
If you would like to see how the elimination method is used in solving some real-world problems, click here.