Answer:
A. x<7
Step-by-step explanation:
The point at x=7 is an open circle, so the sign is <, not ≤
The elimination method works by adding the two equations and eliminating one variable. Then you solve an equation in one variable. Finally, you use substitution or elimination again to find the other variable. Sometimes, by simply adding the equations, a variable is not eliminated. Then you need to multiply one or both equations by a factor to get a variable to be eliminated.
A)
2x - 4y = 8
x + 3y = -11
Adding the equations does not eliminate x or y.
Notice that in the first equation, every coefficient is even. We can divide both sides of the first equation by 2. Then the first term would be x. Instead, let's divide both sides of the first equation by -2. Then the x's will be eliminated.
-x + 2y = -4 <-- The first equation divided by -2
x + 3y = -11 <-- The original second equation. Now we add the equations.
----------------
5y = -15
y = -3
Now that we know y = -3, we substitute it into the first original equation and solve for x.
2x - 4y = 8
2x - 4(-3) = 8
2x + 12 = 8
2x = -4
x = -2
Answer: x = -2; y = -3
B)
We see that the x's will be eliminated by addition. Just add the equations.
-3x + 7y = 9
3x - 7y = 1
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0 + 0 = 10
0 = 10 <---- this is a false statement, so this system of equations has no solution.
Answer:
Step-by-step explanation:
Find and compare the unit costs of the two different bottle sizes.
First:
$2.79/(6 oz) = $0.465/oz
Second:
$10.89/(14 oz) = $0.778/oz
Clearly, the larger (14 oz) bottle is a much better buy
Answer:
<A = 41.4°
Step-by-step explanation:
Recall, SOH CAH TOA
Reference angle = <A
Hypotenuse length = 8
Adjacent length = 6
Since Hypotenuse and Adjacent are involved, we would apply CAH, which is:
Cos A = Adj/Hyp
Plug in the values
Cos A = 6/8
Cos A = 0.75
A = 41.4096221° ≈ 41.4° (nearest tenth)
Answer:
Krista put 0.40 in the first equation meant for the number of stamps.
Step-by-step explanation:
Krista's equation
0.40x+y=45
x+0.55y=18.75
The system of Equation should have been
x + y = 45 (1)
0.40x + 0.55y = 18.75 (2)
From (1)
x=45-y
Substitute x=45-y into (2)
0.40(45 - y) + 0.55y = 18.75
18 - 0.40y + 0.55y = 18.75
Collect like terms and you now have
0.55y - 0.40y = 18.75 - 18
0.15y = 0.75
Divide both sides of the equation by 0.15
y = 5
Substitute y=5 into (1)
x + y = 45
x+5=45
x=45-5
x=40
This shows that the stamps that cost 0.40 cents were 40 while those that cost 0.55 cents were 5 in number.
Krista's error:
Krista put 0.40 in the first equation meant for the number of stamps.
