Download Solving Sytems by Using Elimination

Solving Sytems by Using Elimination
***Sometimes you get an equation with fractions when you solve for one of the
variables in a linear system. These systems may be easier to solve using the linear
combination method.
 Steps to Solving a Linear System by Linear Combinations

Arrange the equations in standard form with like terms in columns.
 Step 1
Step 2
If necessary, make like terms “cancel out” by multiplying one or both

equations by a number.
 Step 3
Add the two equations together.
Solve for the remaining variable.
 Step 4
Step 5
Substitute the value obtained in step four into one of the original

equations.
Solve for the variable.
 Step 6
Step 7
Check.

Example 1: Elimination Using Addition

–x + 2y = -8
4x + 3y = 16
x + 6y = -16
Try These 
1. 3x – 5y = -16
2x – 3y = 8

2x + 5y = 8
2. 2x + y = 18
4x – y = 12
Example 2: Elimination Using Subtraction
1. 3x + y = 5
2x + y = 10
2. 2x – 5y = -6
2x – 7y = -14

Try These 
1. 2x – 6y = 6
2x + 3y = 24
2. 5x + 3y = 22
5x – 2y = 2
Example 3: Put in Standard Form First 
1. y = –x – 4
x–y=2
Try These 
1. 2x = 3y – 11
x + 3y = 8
2. 3x = 4 – y
–y = –2x + 6
2. y = –9 – 4x
–10 – 2y = 4x
Example 4: Use a Linear System as a Real-World Model
1. The sum of two numbers is 48, and their difference is 24.
the numbers?
What are
3. Find two numbers whose sum is 51 and whose difference is 13.
Example 1:
Multiply One Equation to Eliminate
1. 3x + 4y = 6
5x + 2y = -4

2. 2y + y = 23
3x + 2y = 37

Try These 
3. -5x + 3y = 6
Example 2:
x–y=4
4. 2x + y = 5
3x – 2y = 4
Multiply Both Equations to Eliminate 
3. 3x + 4y = -25
2x – 3y = 6
Try These 
3. 2x – 3y = 2
5x + 4y = 28
4. 4x + 3y = 8
3x – 5y = -23

4. 4x – 7y = 10
3x + 2y = 14
Example 3: Use a Linear System as a Real-World Model
1. Eight times a number plus five times another number is -13. The sum of the two numbers is 1.
What are the numbers?
2. Two times a number plus three times another number equals 4. Three times the first number plus
four times the other number is 7. Find the numbers.