Download Warm up Lesson 11

Warm up Lesson 11
1. Is either set of coordinates a solution to the following system
of equations. (3, -7) or (-7, 3)
3x - 2y = 23
4x +4y = -16
2 and 3 solve both system of equations using substitution.
3.
2.
y  x  4

3 x  y  16
Monday, August 04, 2014
x  3 y  4

2 x  y  8
Lesson 10
1. (-4, -20) 2. (5, 2)
3. (9, 2)
4. (5, 3)
5. (-2.3, -9.8)
6. (1, -2)
7. (15, -6)
8. y = -3x + 11
9. y = 2x + 8
10. y = -5x + 11
11. Slope : - 4/3 ; y int: 10
12. slope : 4/3, y int: -7
13. y = x + 4
14. y = -2x +2
15. X = 1.5
16. y = 2x + 14
17. x = -2
18. Y = 2x + 2
19. y = 1/3 x – 6
20. y = -2x + 3
21. Y = 38x + 120
22. 7
Monday, August 04, 2014
Solving system of equations with addition
x + 2y = -2
-6x = 5y + 20
Original equations
6x + y + 4 = 0
Write the equations in standard
= -20
-6x
1[6x+ 5y
+ 5y
= -20]
form.
6x6x
+ +yy== --44
Multiply one or both equations
so you have opposites.
-6x - 5y = 20
6x + y = -4
•Add the equations to obtain a
single equation with one variable
-4y = 16
•Solve for the equation remaining
y = -4
•Plug in the answer above into
one of the original equations
and solve for the other variable.
Check answer with other equation
Monday, August 04, 2014
(0,-4)
-6x = 5y + 20
-6x = 5(-4) + 20
-6x = -20 + 20
x=0
6x + y + 4 = 0
6(0) + -4 + 4 = 0
0 = 0
4x = - 2y - 17
x +x2y += 2y
- 2 = -2
4x
+ 2y+= 2y
-17 =
-1(4x
-17)
x + 2y = -2
-4x - 2y = 17
-3x = 15
x = -5
x + 2y = -2
(-5) + 2y = -2
2y =3 3
y = /2
4x = -2y - 17
4( -5) = - 2(3/2) - 17
-20 = -3 – 17
-20 = -20
(-5,3/2)
Practice Lesson 11 # 1
Original equations
4x = -4y + 8
6x = 2y - 20
Write the equations in standard
4x 4x
+ 4y
+ 4y
= 8= 8
form.
6x
2[6x
– 2y
– 2y
= -20
= -20]
Multiply one or both equations
so you have opposites.
4x + 4y = 8
12x – 4y = -40
•Add the equations to obtain a
single equation with one variable
•Solve for the variable remaining
16 x = -32
x=-2
4x = -4y + 8
•Plug in the answer above into
4(-2) = -4y + 8
one of the original equations
-8 = -4y + 8
and solve for the other variable.
-16 = -4y
y=4
6x = 2y - 20
Check answer with other equation
6(-2) = 2(4) -20
-12 = 8 - 20
Monday, August 04, 2014
-12 = -12
Practice Lesson 11 # 2
Original equations
12x = -2y + 20
6x + y + 4 = 0
Write the equations in standard
form.
Multiply one or both equations
so you have opposites.
12x
12x++2y2y= =2020
+ +yy== -4]
-4
-26x
[6x
12x + 2y = 20
-12x - 2y = 8
•Add the equations to obtain a
single equation with one variable
0 = 28
Since 0 cannot equal 28, there is
no solution to this system, the
lines are parallel
Monday, August 04, 2014
If you get 0 = 0, or any number =
to itself, the lines are dependent
and there are an infinite number
of solutions.
Practice Lesson 11 # 3 & 4
Original equations
x+y=5
y = 2x + 15
2x = -6 + 2y
4x = -12 + 4y
Write the equations in standard
x-2[x
+ y+=y5= 5]
form.
2x – 2y = -6
Multiply one or both equations
so you have opposites.
-2x + +y y= +
2[-2x
= 15
+ 15]
4x – 4y = -12
-2x – 2y = -10
-4x + 2y = + 30
2x – 2y = -6
4x – 4y = -12
•Add the equations to obtain a
single equation with one variable
-4y = -16
-2y = 18
•Solve for the equation remaining
y=4
y = -9
•Plug in the answer above into
one of the original equations
and solve for the other variable.
Check answer with other equation
Monday, August 04, 2014
x+y=5
x+4=5
x =1
2x = -6 + 2y
2(1) = -6 + 2(4)
2 =2
y = 2x + 15
-9 = 2x + 15
-24 = 2x
-12 = x
4x = -12 + 4y
4(-12) = -12 + 4(-9)
-48 = -48
Practice Lesson 11 # 5
Original equations
3x = 4y + 8
3y = -2x + 11
Write the equations in standard
2[3x
3x – –4y4y
= =8 8]
form.
-3[2x
2x + 3y
+ 3y
= =1111]
Multiply one or both equations
so you have opposites.
6x – 8y = 16
-6x - 9y = -33
•Add the equations to obtain a
single equation with one variable
-17y = -17
•Solve for the variable remaining
y= 1
3x = 4y + 8
3x = 4(1) + 8
3x = 4 + 8
3x = 12
x =4
•Plug in the answer above into
one of the original equations
and solve for the other variable.
Check answer with other equation
Monday, August 04, 2014
3y = -2x + 11
3(1) = -2(4) + 11
3 = -8 + 11
3 =3
Practice Lesson 11
6. 5x + y = 2
5x – 3y = 14
(1, -3)
9. 5x – 4y = 23
7x + 8y = 5
(3, -2)
Monday, August 04, 2014
7. 7x – 4y = -10
4y = x – 2
(-2, -1)
10. 10x – 5 = 3y
2x – 3y = 1
( ½ , 0)
8. x = 5 – 9y
4x + 9y = -7
(-4, -1)
11. 5x – 2y = 4
2x + 4y = 16
(2, 3)
Assignment
• Lesson 11
Monday, August 04, 2014