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g100num [7]
3 years ago
11

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 5x+7=2y and

y-9x=23
A) {}
B) 1 solution
C) Infinite
Mathematics
2 answers:
Luda [366]3 years ago
7 0

Answer:

The correct option is option B. It has one solution, and it's x=-3

Step-by-step explanation:

We have the following system of equations:

5x+7 = 2y                        (1)

y-9x=23                            (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

5x + 7 = 18x + 46

Step 3: Solve for x:

7 - 46 = 18x - 5x

-39 = 13x

x= -3

So the correct option is option B. It has one solution, and it's x=-3

jeka57 [31]3 years ago
7 0

Answer: Option B

The system has 1 solution

Step-by-step explanation:

We must solve the following system of equations

5x+7=2y\\\\y-9x=23  

To solve it, clear y from the second equation and then substitute in the first equation

y=23 + 9x

Now substitute in the first equation

5x+7=2(23 + 9x)\\\\5x +7 = 46 + 18x\\\\5x -18x = 46-7\\\\-13x = 39\\\\x = -\frac{39}{13}\\\\x=-3

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FIND THE VALUEOF THE VARIBLE AND FILL THE BLANK.
ludmilkaskok [199]

Answer:

f = 2

g = 8

h = -9

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m = 1

Step-by-step explanation:

Equation 1:

23f - 17 = 29

Add 17 to both sides. This undoes the -17.

23f = 29 + 17

Add 17 to 29 to get 46.

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Divide both sides by 23. This undoes the multiplication by 23.

f = 46/23

Divide 46 by 23 to get 2.

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Equation 2:

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Divide both sides by 2. This undoes the multiplication by 2.

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Divide 56 by 2 to get 28.

3g + 4 = 28

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3g = 24

Divide both sides by 3. This undoes the multiplication by 3.

g = 24/3

Divide 24 by 3 to get 8.

g = 8

Equation 3:

h + 9 = 0

Subtract 9 from both sides. This undoes the +9.

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Any number subtracted from 0 gives its negation.

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Equation 4

3(k - 8) = 96

Divide both sides by 3. This undoes the multiplication by 3.

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Divide 96 by 3 to get 32.

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Add 5 to both sides. This undoes the -5

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5m = 5

Divide both sides by 5. This undoes the multiplication by 5

m = 5/5

Anything divided by itself gives you 1.

m = 1

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