![Page 1: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/1.jpg)
Dr. Fowler CCM
Solving Systems of EquationsBy Elimination – Easier
![Page 2: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/2.jpg)
Solving a system of equations by elimination using addition and subtraction.
Step 1: Put the equations in Standard Form.
Step 2: Determine which variable to eliminate.
Step 3: Add or subtract the equations.
Step 4: Plug back in to find the other variable.
Step 5: Check your solution.
Standard Form: Ax + By = C
Look for variables that have the
same coefficient.
Solve for the variable.
Substitute the value of the variable
into the equation.
Substitute your ordered pair into
BOTH equations.
![Page 3: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/3.jpg)
1) Solve the system using elimination.
x + y = 5
3x – y = 7Step 1: Put the equations in
Standard Form.
Step 2: Determine which variable to eliminate.
They already are!
The y’s have the same
coefficient.
Step 3: Add or subtract the equations.
Add to eliminate y.
x + y = 5
(+) 3x – y = 7
4x = 12
x = 3
![Page 4: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/4.jpg)
1) Solve the system using elimination.
Step 4: Plug back in to find the other variable.
x + y = 5
(3) + y = 5
y = 2
Step 5: Check your solution.
(3, 2)
(3) + (2) = 5
3(3) - (2) = 7
The solution is (3, 2). What do you think the answer would be if you solved using substitution?
x + y = 5
3x – y = 7
![Page 5: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/5.jpg)
EXAMPLE #2:
STEP 2: Use subtraction to eliminate 5x. 5x + 3y =11 5x + 3y = 11
-(5x - 2y =1) -5x + 2y = -1
5x + 3y = 11
5x = 2y + 1
Note: the (-) is distributed.
STEP 3: Solve for the variable. 5x + 3y =11
-5x + 2y = -15y =10 y = 2
STEP1: Write both equations in Ax + By = C form. 5x + 3y =11 5x - 2y =1
![Page 6: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/6.jpg)
STEP 4: Solve for the other variable by substitutingy = 2 into either equation.5x + 3y =11
5x + 3(2) =11 5x + 6 =11 5x = 5 x = 1
5x + 3y = 11
5x = 2y + 1
The solution to the system is (1, 2).
![Page 7: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/7.jpg)
3) Solve the system using elimination.
4x + y = 7
4x – 2y = -2Step 1: Put the equations in
Standard Form.They already are!
Step 2: Determine which variable to eliminate.
The x’s have the same
coefficient.
Step 3: Add or subtract the equations.
Subtract to eliminate x.
4x + y = 7
(-) 4x – 2y = -2
3y = 9
y = 3Remember to “keep-change-
change”
![Page 8: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/8.jpg)
3) Solve the system using elimination.
Step 4: Plug back in to find the other variable.
4x + y = 7
4x + (3) = 7
4x = 4
x = 1
Step 5: Check your solution.
(1, 3)
4(1) + (3) = 7
4(1) - 2(3) = -2
4x + y = 7
4x – 2y = -2
![Page 9: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/9.jpg)
4) Solve the system using elimination.
y = 7 – 2x
4x + y = 5Step 1: Put the equations in
Standard Form.2x + y = 7
4x + y = 5
Step 2: Determine which variable to eliminate.
The y’s have the same
coefficient.
Step 3: Add or subtract the equations.
Subtract to eliminate y.
2x + y = 7
(-) 4x + y = 5
-2x = 2
x = -1
![Page 10: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/10.jpg)
4) Solve the system using elimination.
Step 4: Plug back in to find the other variable.
y = 7 – 2x
y = 7 – 2(-1)
y = 9
Step 5: Check your solution.
(-1, 9)
(9) = 7 – 2(-1)
4(-1) + (9) = 5
y = 7 – 2x
4x + y = 5
![Page 11: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/11.jpg)
Elimination using Addition
5) Solve the system
x - 2y = 5
2x + 2y = 7
Lets add both equations to each other
![Page 12: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/12.jpg)
Elimination using Addition
5) Solve the system
x - 2y = 5
2x + 2y = 7
Lets add both equations to each other+
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
![Page 13: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/13.jpg)
Elimination using Addition
5) Solve the system
x - 2y = 5
2x + 2y = 7
Lets add both equations to each other+
3x = 12x = 4
ANS: (4, y)
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
![Page 14: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/14.jpg)
Elimination using Addition
5) Solve the system
x - 2y = 5
2x + 2y = 7
ANS: (4, y)
Lets substitute x = 4 into this equation.
4 - 2y = 5 Solve for y - 2y = 1
y = 12
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
![Page 15: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/15.jpg)
Elimination using Addition
5) Solve the system
x - 2y = 5
2x + 2y = 7
Answer: (4, )
Lets substitute x = 4 into this equation.
4 - 2y = 5 Solve for y - 2y = 1
y = 12 1
2
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
![Page 16: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/16.jpg)
Elimination using Addition
3x + y = 14
4x - y = 7
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
5) Solve the system
![Page 17: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/17.jpg)
Elimination using Addition
3x + y = 14
4x - y = 7
7x = 21x = 3
ANS: (3, y)
+
5) Solve the system
![Page 18: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/18.jpg)
Elimination using Addition
Answer: (3, 5 )
3x + y = 14
4x - y = 7
Substitute x = 3 into this equation
3(3) + y = 149 + y = 14
y = 5
NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.
5) Solve the system
![Page 19: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/19.jpg)
Excellent Job !!!Well Done
![Page 20: Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649e925503460f94b97671/html5/thumbnails/20.jpg)
Stop NotesDo Worksheet