1. 7-3: Solving Systems of Equations using Elimination
Steps:
1. Place both equations in Standard Form, Ax + By = C.
2. Determine which variable to eliminate with Addition or Subtraction.
3. Solve for the variable left.
4. Go back and use the found variable in step 3 to find second variable.
5. Check the solution in both equations of the system.

2. 5x + 3y = 11
5x = 2y + 1
EXAMPLE #1:
STEP1: Write both equations in Ax + By = C
form x + 3y =11
5x - 2y =1
STEP 2: Use subtraction to eliminate 5x x + 3y = x + 3y = 11
-(5x - 2y =1) x + 2y = -1
Note: the (-) is distributed.
STEP 3: Solve for the variable.
5x + 3y =11
-5x + 2y = -1
5y = y = 2

3. The solution to the system is (1,2).
5x + 3y = 11
5x = 2y + 1
STEP 4: Solve for the other variable by substituting
into either equation.
5x + 3y =11
5x + 3(2) =11
5x + 6 =11
5x = 5
x = 1
The solution to the system is (1,2).

4. 5x + 3y = 11 5x = 2y + 1 5(1) + 3(2) =11 5(1) = 2(2) + 1 5 + 6 =11
Step 5: Check the solution in both equations.
The solution to the system is (1,2).
5x + 3y = 11
5(1) + 3(2) =11
5 + 6 =11
11=11
5x = 2y + 1
5(1) = 2(2) + 1
5 = 4 + 1
5=5

5. Solving Systems of Equations using Elimination
Steps:
1. Place both equations in Standard Form, Ax + By = C.
2. Determine which variable to eliminate with Addition or Subtraction.
3. Solve for the remaining variable.
4. Go back and use the variable found in step 3 to find the second variable.
5. Check the solution in both equations of the system.

6. Example #2:
x + y = 10
5x – y = 2
Step 1: The equations are already in standard
form: x + y = 10
5x – y = 2
Step 2: Adding the equations will eliminate y.
x + y = x + y = 10
+(5x – y = 2) +5x – y = +2
Step 3: Solve for the variable.
x + y = 10
+5x – y = +2
6x = 12
x = 2

7. Solution to the system is (2,8).
x + y = 10
5x – y = 2
Step 4: Solve for the other variable by
substituting into either equation.
x + y = 10
2 + y = 10
y = 8
Solution to the system is (2,8).

8. x + y =10 5x – y =2 2 + 8 =10 5(2) - (8) =2 10 – 8 =2 10=10 2=2
Step 5: Check the solution in both equations.
Solution to the system is (2,8).
x + y =10
2 + 8 =10
10=10
5x – y =2
5(2) - (8) =2
10 – 8 =2
2=2

9. NOW solve these using elimination:1. 2.
2x + 4y =1
x - 4y =5
2x – y =6
x + y = 3

10. NOW solve these using elimination:1. 2.
2x + 4y =1
x - 4y =5
2x – y =6
x + y = 3
Solution (2,- 3 4 )
Solution (3,0)