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Ira Lisetskai [31]
3 years ago
11

3x + 8y = 12 2x + 2y = 3 Part A: Create an equivalent system of equations by replacing one equation with the sum of that equatio

n and a multiple of the other. Show the steps to do this. (6 points) Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)
Mathematics
1 answer:
love history [14]3 years ago
7 0
Ok here is what I think.
Let us first number these statements, as #1, and #2.
First statement: 3x + 8y = 12 (1)
Second Statement: 2x + 2y = 3 (2)
Now, we can work from this.
We want to make one of the equations be equal to 0 so that at the end when we check they can be equal to each other.
Let us use 4.
3x+8y=12      1-8x-8y=-12    2
This gives us:-5x = 0          
Now we should try and isolate x so we can substitute it into one of the equations.
We have -5x=0
and x=0
3(0)+8y=12
8y=12
y=12/8
y=3/2
Plug in these new equations
y=3/2 and y=0 into any of the first equations
 3x+8y=12                3(0)+8(3/2)= 12       8(3/2)=12                 4(3)=12                    12=12                           
Now we know it works, thats our check^^
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Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each. Daniel has $20 to
grigory [225]

The system of inequalities are x + y ≥ 7 and 3.75x + 1y ≤ 20 The one possible solution is 4 cupcakes and 3 donuts.

<u>Solution:</u>

Given, Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each.  

Daniel has $20 to spend and must buy a minimum of 7 cupcakes and donuts altogether.  

⇒ "x" represents the number of cupcakes purchased

⇒ "y" represents the number of donuts purchased,  

we have to write and solve a system of inequalities graphically and determine one possible solution.

Now, he should buy minimum 7 items, then x + y ≥ 7 ⇒ (1)

And, he has $20, so his maximum purchase is $20 then, 3.75x + 1y ≤ 20 ⇒ (2)

Now, suppose that he took 5 cupcakes, then he must take at least 2 donuts to satisfy (1)

So, substitute x and y values in (2)

⇒ 3.75(5) + 1(2) ≤ 20

⇒ 20.75 ≤ 20 ⇒ condition failed

So he can take maximum of 4 cupcakes only, and subsequently he has to take minimum of 3 donuts.

Hence, the one possible solution is 4 cupcakes and 3 donuts

7 0
3 years ago
Type the correct answer in each box. If necessary, use / for the fraction bar(s).
spayn [35]

Answer:X=5/6 Y=8/5

Step-by-step explanation:

-6x +5y=3

+6x

5y=6x+3 (divide each number by 5)

Y=6/5x + 3/5 (Plug that into your x equation)

12x+15 (6/5x + 3/5) =34

(Multiply 15 by the numbers in the brackets you can break it down and do 15•6 divided by 5 )

15•6=90 divided by 5=18x

15•3= 45 divided by 5=9

(Add like variables)

12x+18x=30x

30x+9=34

(Subtract 9 from itself do the same to 34)

9-9= 0

34-9=25

Divide 30 by itself to get x by itself then divide 25 by 30

25 divided by 30= 5/6

X=5/6 (plug that into the y equation)

Y=6/5•5/6+3/5

Multiply 6/5 and 5/6 straight across because this is multiplication you don't need like denominators

6/5•5/6=30/30=1

Y=1+3/5

1/1 + 3/5

Here you need to have like denominators because it is addition so just use 5

5•1=5

5/5+3/5=8/5

Y=8/5

5 0
2 years ago
Through: (4, -3), perp. to y=-2x + 1
larisa86 [58]

Step-by-step explanation:

y = -2x + 1. => Slope = -2

Then the perpendicular line will have a slope of -1/(-2) = 0.5.

We have y = 0.5x + c.

When x = 4, y = -3.

=> (-3) = 0.5(4) + c, c = -5.

Hence the answer is y = 0.5x - 5. (C)

7 0
2 years ago
Find g. (-9)<br> g(+)= r^2 + 3r
oee [108]

Answer:

  • g(-9) = 64

Step-by-step explanation:

<u>Given function:</u>

  • g(r) = r² + 3r

<u>Find g(-9):</u>

  • g(-9) = (-9)² + 3(-9) = 81 - 27 = 64
7 0
2 years ago
What is the solution to 2(2x +1) = 0.5(2x - 14)?​
Leona [35]
Where are the options
3 0
2 years ago
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