Systems of equations - Elimination method - …...10 x + 10x x +
Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually...
-
Upload
christian-sandoval -
Category
Documents
-
view
214 -
download
0
Transcript of Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually...
![Page 1: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/1.jpg)
Simultaneous Equations
elimination
![Page 2: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/2.jpg)
What are they?
• Simply 2 equations– With 2 unknowns– Usually x and y
• To SOLVE the equations means we find values of x and y that– Satisfy BOTH equations [work in]– At same time [simultaneously]
![Page 3: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/3.jpg)
Elimination Method
2x – y = 1
3x + y = 9
We have the same number of y’s in each
If we ADD the equations, the y’s disappear+
5x = 10 Divide both sides by 5
x = 2
AB
Substitute x = 2 in equation A2 x 2 – y = 1
4 – y = 1y = 3
Answerx = 2, y = 3
![Page 4: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/4.jpg)
Elimination Method
5x + y = 17
3x + y = 11
We have the same number of y’s in each
If we SUBTRACT the equations, the y’s disappear
-
2x = 6 Divide both sides by 2
x = 3
AB
Substitute x = 3 in equation A5 x 3 + y = 17
15 + y = 17y = 2
Answerx = 3, y = 2
![Page 5: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/5.jpg)
Elimination Method
2x + 3y = 9
2x + y = 7
We have the same number of x’s in each
If we SUBTRACT the equations,the x’s disappear
-
2y = 2 Divide both sides by 2
y = 1
AB
Substitute y = 1 in equation A2x + 3 = 9
2x = 6x = 3
Answerx = 3, y = 1
![Page 6: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/6.jpg)
Elimination Method
4x - 3y = 14
2x + 3y = 16
We have the same number of y’s in each
If we ADD the equations,the y’s disappear
+
6x = 30 Divide both sides by 6
x = 5
AB
Substitute x = 5 in equation A20 – 3y = 14
3y = 6y = 2
Answerx = 5, y = 2
![Page 7: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/7.jpg)
Basic steps
• Look at equations
• Same number of x’s or y’s?
• If the sign is different, ADD the equations otherwise subtract tem
• Then have ONE equation
• Solve this
• Substitute answer to get the other
• CHECK by substitution of BOTH answers
![Page 8: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/8.jpg)
What if NOT same number of x’s or y’s?
5x + 2y = 173x + y = 10
-x = 3
In B
AB
5 x 3 + 2y = 1715 + 2y = 17
y = 1
Answerx = 3, y = 1
If we multiply A by 2 we get 2y in each
5x + 2y = 176x + 2y = 20
B
A
![Page 9: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/9.jpg)
What if NOT same number of x’s or y’s?
3x + 6y = 214x - 2y = 8
+15x = 45
In B
AB
3 x 3 + 6y = 216y = 12
y = 2
Answerx = 3, y = 2
If we multiply A by 3 we get 6y in each
3x + 6y = 2112x - 6y = 24
B
A
x = 3
![Page 10: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/10.jpg)
…if multiplying 1 equation doesn’t help?
3x + 7y = 265x + 2y = 24
-29y = 58
In B
AB
5x + 2 x 2 = 245x = 20
x = 4
Answerx = 4, y = 2
Multiply A by 5 & B by 3, we get 15x in each
15x + 35y = 13015x + 6y = 72B
A
y = 2
Could multiply A by 2 & Bby 7 to get 14y in each
![Page 11: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/11.jpg)
…if multiplying 1 equation doesn’t help?
3x - 2y = 75x + 3y = 37
+19x = 95
In B
AB
5 x 5 + 3y = 373y = 12
y = 4
Answerx = 5, y = 4
Multiply A by 3 & B by 2, we get +6y & -6y
9x – 6y = 2110x + 6y = 74B
A
x = 5
Could multiply A by 5 & Bby 3 to get 15x in each
![Page 12: Simultaneous Equations elimination. What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of.](https://reader034.fdocuments.net/reader034/viewer/2022051819/5515175955034673228b4c9d/html5/thumbnails/12.jpg)
Independent Practice
• Solve #2 a, b, c
• #4 d, e , f ,g