3x – 6y = -3 2x + 4y = 30 do now. homework solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32...
TRANSCRIPT
![Page 1: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/1.jpg)
3x – 6y = -3
2x + 4y = 30
Do Now
![Page 2: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/2.jpg)
Homework Solutions
1) x + y = -9 5x + 5y = -455x – 2y = 32 – 5x – 2y = 32
7y = -77 y = -11
x + y = -9 x + (-11) = -9 x – 11 = -9 x = 2
Solution: (2, -11)
![Page 3: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/3.jpg)
Homework Solutions
4) 2x + y = 3 -8x – 4y = -12-4x – 4y = -8 – -8x – 8y = -16
4y = 4 y = 1
2x + y = 32x + 1 = 3 2x = 2 x = 1
Solution: (1, 1)
![Page 4: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/4.jpg)
Homework Solutions7) 5x + 3y = -10 15x + 9y = -30
3x + 5y = -6 – 15x + 25y = -30 -16y = 0
y = 05x + 3y = -105x + 3(0) = -105x = -10 x = -2
Solution: (-2, 0)
![Page 5: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/5.jpg)
Homework Solutions10) 3x + 2y = -26 12x + 8y = -
104 4x – 5y = -4 – 12x – 15y = -12
23y = -92 y = -4
3x + 2y = -263x + 2(-4) = -263x – 8 = -263x = -18
x = -6Solution: (-6, -4)
![Page 6: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/6.jpg)
SubstitutionIf x = 5, find the value of 3x.
The substitution property says that a quantity can be substituted for its equal in any expression.
We can use this property to solve systems of equations.
![Page 7: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/7.jpg)
Solving Systems Using Substitution
Steps:
1) Find the equation that is solved for a variable.
(y = or x = )
2) Substitute into the OTHER equation.
3) Solve the new equation for the variable.
4) Substitute and solve for the other variable.
![Page 8: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/8.jpg)
Solve using substitution.
y = 3x
x + 2y = – 21
![Page 9: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/9.jpg)
Solve using substitution.
y = x – 4
3x + y = 8
![Page 10: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/10.jpg)
![Page 11: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/11.jpg)
x = 4y + 5
x – 3y = – 2
![Page 12: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/12.jpg)
4x + 5y = 11
y = 3x – 13
![Page 13: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/13.jpg)
![Page 14: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/14.jpg)
y = 4x – 1
y = 2x – 5
![Page 15: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/15.jpg)
3x + 2y = -9
x = y – 13
![Page 16: 3x – 6y = -3 2x + 4y = 30 Do Now. Homework Solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32 – 5x – 2y = 32 7y = -77 y = -11 x + y = -9 x + (-11) = -9](https://reader033.vdocuments.net/reader033/viewer/2022061422/5697bfc61a28abf838ca737a/html5/thumbnails/16.jpg)
Homework
Worksheet pgs. 68 & 69 #’s 2, 8, 10
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