Transcript Solving Systems of Equations using Substitution

3-2: 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.
EXAMPLE #1:
5x + 3y = 11
5x = 2y + 1
STEP1: Write both equations in Ax + By = C
form.
5x + 3y =1
5x - 2y =1
STEP 2:
Use subtraction to eliminate 5x.
5x + 3y =11
5x + 3y = 11
-(5x - 2y =1)
-5x + 2y = -1
Note: the (-) is distributed.
STEP 3:
Solve for the variable.
5x + 3y =11
-5x + 2y = -1
5y =10
y=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).
5x + 3y= 11
5x = 2y + 1
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
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.
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 = 10
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
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).
x + y = 10
5x – y = 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
Using Elimination to Solve a
Word Problem:
Two angles are supplementary. The
measure of one angle is 10 degrees
more than three times the other.
Find the measure of each angle.
Using Elimination to Solve a
Word Problem:
Two angles are supplementary. The
measure of one angle is 10 more
than three times the other. Find the
measure of each angle.
x = degree measure of angle #1
y = degree measure of angle #2
Therefore x + y = 180
Using Elimination to Solve a
Word Problem:
Two angles are supplementary. The
measure of one angle is 10 more
than three times the other. Find the
measure of each angle.
x + y = 180
x =10 + 3y
Using Elimination to Solve a
Word Problem:
Solve
x + y = 180
x =10 + 3y
x + y = 180
-(x - 3y = 10)
4y =170
y = 42.5
x + 42.5 = 180
x = 180 - 42.5
x = 137.5
(137.5, 42.5)
Using Elimination to Solve a
Word Problem:
The sum of two numbers is 70
and their difference is 24. Find
the two numbers.
Using Elimination to Solve a
Word problem:
The sum of two numbers is 70
and their difference is 24. Find
the two numbers.
x = first number
y = second number
Therefore, x + y = 70
Using Elimination to Solve a
Word Problem:
The sum of two numbers is 70
and their difference is 24. Find
the two numbers.
x + y = 70
x – y = 24
Using Elimination to Solve a
Word Problem:
x + y =70
x - y = 24
2x = 94
x = 47
47 + y = 70
y = 70 – 47
y = 23
(47, 23)