Download Lesson 10 Solving system of equations by substitution

Lesson 10
Solving system of equations by
substitution
August 6, 2014
Warm up Lesson 10
1. Find the x-intercept, y-intercept
and slope of the following equation.
-3y + 6x + 9 = 0
2. Translate the following equation 2
units down and 3 units to the right.
4. To install a security system in my
house there was an initial fee of $115
plus the $35 monthly fee. Write an
equation that relates time (x) to the
amount of money spent (y).
2y – 3x = 4
3. Graph the following equation
5. Graph the following equation
y = -2x
2y + 3x = 4
y
y
x
6. Change title of homework from Lesson 1 to Lesson 10.
x
Answers to Lesson 9
1. -12
2. 2
3. -2
4. -8
5. Y = - 4x + 29
6. y = 4x + 2 7. y = 2x
8. Y = - ½ x – 1
9. y = - 3/2x + 7/2
11. Y = 2x – 14
12. slope: - 2/3, y-int: 10
14. Y = - 2 x + 2
15. y = -3
17. Y = 8x + 7
20. y = 2x + 3
18.
19.
10. y = -2/3 x - 2
13. – 5/2
16. y = 3x + 16
21.
(100  p)n
100
22. B
Consistent systems.
Consistent systems
Exactly one solution
y
Lines intersect and may or may
not be perpendicular
Different slopes
x
Inconsistent system
• No solution
• Lines are parallel
• Same slopes,
different y intercepts
y
x
Dependent system
• Infinite number of
solutions.
• Lines are coincident
• Same slopes, same
y intercepts
y
x
Solving system of equations by substitution
x–y=2
6x – y = -4
4x – 3y = 11
2x + 2y = 15
1. Pick one equation and
solve for one variable.
x–y=2
6x – y = -4
x=y+2
6x = y – 4
y = 6x + 4
2. Using the other
equation, substitute
3. Solve for the
remaining variable.
4x – 3y = 11
2x + 2y = 15
4(y + 2) – 3y = 11
2x + 2(6x+4) = 15
2x + 12x + 8 = 15
4y + 8 – 3y = 11
14x + 8 = 15
y + 8 = 11
y=3
4. Substitute the value
found in step 3, into
equation used in step 1
6x – y = - 4
x–y=2
6(1/2) – y = -4
x–3=2
3 –y = -4
x =5
(5, 3)
y=7
14x = 7
x=½
( ½ , 7)
5. Check you answer
using the same equation
in step 2.
4x – 3y = 11
2x + 2y = 15
4(5) – 3(3) = 11
2(1/2) + 2(7) = 15
20 – 9 = 11
1 + 14 = 15
11 = 11
15 = 15
Therefore the solution that
will answer both of these
equations is (5,3)
Therefore the solution that
will answer both of these
equations is ( ½ ,7)
Solving system of equations by substitution
2x – y = 16
-x + 2y = -8
1. Pick one equation and
solve for one variable.
5. Check your answer with
equation used in step 2.
2x – y = 16
-x + 2y = -8
2y = x -8
2(8) – (0) = 16
2y + 8 = x
16 – 0 = 16
16 = 16
2. Using the other
equation, substitute
2x – y = 16
2(2y + 8) - y = 16
3. Solve for the
remaining variable.
4y + 16 – y = 16
3y = 0
y=0
-x + 2y = -8
4. Substitute the value
found in step 3, into
equation used in step 1
-x + 2(0) = -8
- x = -8
x=8
(8, 0)
Solving system of equations by substitution
5x – 3y = -11
1. Pick one equation and
solve for one variable.
x – 2y = 2
5. Check your answer with
equation used in step 2.
x – 2y = 2
5x – 3y = -11
x = 2y + 2
5(-4) – 3(-3) = -11
-20 + 9 = -11
2. Using the other
equation, substitute
3. Solve for the
remaining variable.
5x – 3y = -11
- 11 = - 11
5(2y + 2) – 3y = -11
10y + 10 – 3y = -11
7y + 10 = -11
7y = -21
y = -3
x – 2y = 2
4. Substitute the value
found in step 3, into
equation used in step 1
x – 2(-3) = 2
x+6=2
x = -4
(-4, -3)
On your own. Solve each system of
equation below by substitution method.
4.
1.
y = 2x
(4, 8)
y = 2x – 5
4x – y = 7
x + y = 12
(1,-3)
5.
2.
-2x + 3y = 14
2x – 3y = 12
x = 4y + 1
(9,2)
X + 2y = 7
(-1,4)
6.
3.
x–y=3
y = -x + 5
x – 4y = 10
(6,-1)
6x + 4y = 13
(2 ½ , - ½ )
Homework
• Lesson 10 show work to get credit