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.

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.

Replace x with 2 Simplify Subtract 6 from both sides of the equation Simplify Divide both sides of the equation by 2 Simplify

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).

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).