using Elimination Steps 1 Place both equations in Standard Form A x B y C 2 Determine which variable to eliminate with Addition or Subtraction 3 Solve for the variable left ID: 273438
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Slide1
3-2: Solving Systems of Equations using Elimination
Steps:
1. Place both equations in Standard Form, A
x
+ B
y
= 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.Slide2
EXAMPLE #1:
STEP 2:
Use subtraction to eliminate 5
x
. 5x + 3y =11 5x + 3y = 11 -(5x - 2y =1) -5x + 2y = -1
5x + 3y = 115x = 2y + 1
Note: the (-) is distributed.
STEP 3: Solve for the variable. 5x + 3y =11 -5x + 2y = -1 5y =10 y = 2
STEP1:
Write both equations in A
x
+ B
y
= C
form. 5
x
+ 3
y
=1
5
x
- 2
y
=1Slide3
STEP 4:
Solve for the other variable by substituting
into either equation.
5
x + 3y =11 5x + 3(2) =11 5x + 6 =11 5x = 5 x = 15x + 3y = 115
x = 2y + 1The solution to the system is (1,2).Slide4
5
x
+ 3
y= 11
5x = 2y + 1Step 5: Check the solution in both equations.5x + 3y = 11
5(1) + 3(2) =11 5 + 6 =11 11=115x = 2y + 1
5(1) = 2(2) + 1 5 = 4 + 1 5=5
The solution to the system is (1,2).Slide5
Solving Systems of Equations using Elimination
Steps:
1. Place both equations in Standard Form, A
x
+ 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.Slide6
Example #2:
x
+
y
= 10 5x – y = 2Step 1: The equations are already in standard form: x + y = 10
5x – y = 2Step 2: Adding the equations will eliminate y. x +
y = 10 x + y = 10
+(5x – y = 2)
+5x – y = +2Step 3: Solve for the variable. x
+ y = 10 +5
x
–
y
= +2
6
x
= 12
x
= 2Slide7
x
+
y
= 10
5x – y = 2Step 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).Slide8
x
+
y
= 10
5x – y = 2x + y =102 + 8 =10 10=10
5x – y =2 5(2) - (8) =2 10 – 8 =2 2=2
Step 5:
Check the solution in both equations.Solution to the system is (2,8).Slide9
NOW solve these using elimination:
1.
2.
2x + 4y =1 x - 4
y =52x – y =6 x +
y = 3Slide10
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
.Slide11
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 #2Therefore x + y = 180Slide12
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 = 180x =10 + 3ySlide13
Using Elimination to Solve a Word Problem:
Solve
x
+
y = 180x =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)Slide14
Using Elimination to Solve a Word Problem:
The sum of two numbers is 70 and their difference is 24. Find the two numbers
.Slide15
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 numbery = second numberTherefore, x + y = 70Slide16
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 = 70x – y = 24Slide17
Using Elimination to Solve a Word Problem:
x
+
y
=70x - y = 24 2x = 94 x = 4747 + y = 70
y = 70 – 47 y = 23(47, 23)Slide18
Now you Try to Solve These Problems Using Elimination.
Solve
Find two numbers whose sum is 18 and whose difference is 22.
The sum of two numbers is 128 and their difference is 114. Find the numbers.