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3x – 6y = -3 2x + 4y = 30 do now. homework solutions 1) x + y = -9 5x + 5y = -45 5x – 2y = 32...

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  • 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
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3x – 6y = -3 2x + 4y = 30 Do Now

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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

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

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

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

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

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

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

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

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

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
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

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

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
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

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

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

Homework

Worksheet pgs. 68 & 69 #’s 2, 8, 10

Permission Slips Due Wednesday!!


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