1 HW: pgs. 256-257 #11-27odd, 28-31 Weeks Money Saved ($) 28. y = 5x + 25 28. y = 8x + 16 29.Answer:...
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Transcript of 1 HW: pgs. 256-257 #11-27odd, 28-31 Weeks Money Saved ($) 28. y = 5x + 25 28. y = 8x + 16 29.Answer:...
HW: pgs. 256-257 #11-27odd, 28-31
Weeks
Mo
ne
y S
ave
d ($
)
28. y = 5x + 2528. y = 8x + 1629. Answer: 3 weeks
1 2 3 4 5
30. y = 15x + 1028. y = -20x + 15029. Answer: 4 minutes
He
igh
t (m
)
Minutes
605040302010
16014012010080604020
1 2 3 4 5
Substitution: a method to solve a system of equations.
A. Use substitution to solve the system of equations.x = 4y4x – y = 75
Answer: (20, 5)
5-2 Substitution
Step 1: Since x = 4y, substitute 4y for x in the 2nd equation.
4(4y) – y = 75
16y – y
=
75
15y
=
75
y = 5
Step 2: Use x = 4y to find the value of x.
x = 4y
x = 4(5)
x = 20
B. Use substitution to solve the system of equations.4x + y = 12–2x – 3y = 14
Answer: (5, -8)
First, solve the first equation for y since the coefficient of y is 1. 4x + y = 12 y = -4x + 12
Then find the value of x by substituting -4x + 12 for y in the second equation.
–2x – 3y
=
14
–2x – 3(-4x+12)
=
14
–2x +12x – 36
=
14
10x – 36
=
14
10x
=
50
x = 5
Lastly, substitute 5 for x in either equation to find the value of y.
y = -4x + 12
y = -4(5) + 12
y = -20 + 12
y = –8
Use substitution to solve the system of equations.A. 2a + 2b = 8 a + b = –2
Answer: No solution
B. 6x – 2y = -4 y = 3x + 2
Answer: Infinitely many
a = -b – 2
2(-b – 2) + 2b = 8
-2b – 4 + 2b = 8
-4 = 8
6x – 2(3x + 2) = -4
6x – 6x – 4 = -4
-4 = -4
1. A
2. B
3. C
4. D
Answer: 2 mL of 10% HCl solution, 8 mL of 40% HCl solution
CHEMISTRY Michael needs 10 milliliters of 34% HCl (hydrochloric acid) solution for a chemistry experiment. There is a bottle of 10% HCl solution and a bottle of 40% HCl solution in the lab. How much of each solution should he use to obtain the required amount of 34% HCl solution? (Think back to chapter 2… this time we will use 2 equations instead)
Given information
10 mL 34% HCL
x mL 10% HCL
y mL 40% HCL
System of Equations
x + y = 10
0.10x + 0.40y = 0.34(10)
Solve
y = 10 – x
0.10x + 0.40(10 – x) = 3.4
0.1x + 4 – 0.4x = 3.4
-0.3x = -6
x = 2
y = 10 – x
y = 10 – 2
y = 8
1. A
2. B
3. C
4. D
Amy and Rachel are both saving money for a summer vacation. Amy has already saved $100 and plans to save $25 per week until the trip. Rachel has $75 and plans to save $30 per week. In how many weeks will they have the same amount of money? Graph the system of equations to find the answer. (Hint: Go by 25 for the y scale).
Use may use Graphing calculator:
1. Enter equations in y=
2. 2nd [Calc] 5 Enter Enter EnterAnswer: 5 weeks
12-9 Honors Algebra Warm-up