HW: pgs. 256-257 #11-27odd, 28-31
60
50
40
30
20
10
30. y = 15x + 10
28. y = -20x + 150
29. Answer: 4 minutes
Height (m)
Money Saved ($)
28. y = 5x + 25
28. y = 8x + 16
29. Answer: 3 weeks
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2
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Weeks
4
5
160
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20
1 2 3 4
Minutes
5
5-2 Substitution
Substitution: a method to solve a system of equations.
A. Use substitution to solve the system of equations.
x = 4y
4x – y = 75
Step 1: Since x = 4y,
substitute 4y for x
in the 2nd equation.
Step 2: Use x = 4y to find the
value of x.
x = 4y
4(4y) – y = 75
x = 4(5)
16y – y = 75
x = 20
15y = 75
y=5
Answer: (20, 5)
B. Use substitution to solve the system of equations.
4x + y = 12
–2x – 3y = 14
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
Answer: (5, -8)
Use substitution to solve the system of equations.
A. 2a + 2b = 8
B. 6x – 2y = -4
a + b = –2
y = 3x + 2
a = -b – 2
2(-b – 2) + 2b = 8
-2b – 4 + 2b = 8
6x – 2(3x + 2) = -4
6x – 6x – 4 = -4
-4 = -4
-4 = 8
Answer: No solution
Answer: Infinitely many
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
Solve
10 mL 34% HCL
y = 10 – x
y = 10 – x
x mL 10% HCL
0.10x + 0.40(10 – x) = 3.4
y = 10 – 2
y mL 40% HCL
0.1x + 4 – 0.4x = 3.4
y=8
System of Equations
x + y = 10
0.10x + 0.40y = 0.34(10)
1.
-0.3x = -62.
x = 23.
4.
A
B
C
D
Answer: 2 mL of 10% HCl solution, 8 mL of 40% HCl solution
12-9 Honors Algebra Warm-up
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 Enter
1.
2.
3.
4.
A
B
C
D
Answer: 5 weeks