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3 years ago

Solve the following system of equations: y=6-x y=x^2-6x+6

Mathematics

1 answer:

nevsk [136]3 years ago

4 0

Answer:

(0, 6 ) and (5, 1 )

Step-by-step explanation:

Given the 2 equations

y = 6 - x → (1)

y = x² - 6x + 6 → (2)

Substitute y = x² - 6x + 6 into (1)

x² - 6x + 6 = 6 - x ( subtract 6 - x from both sides )

x² - 5x = 0 ← factor out x from each term on the left side

x(x - 5) = 0

Equate each factor to zero and solve for x

x = 0

x - 5 = 0 ⇒ x = 5

Substitute these values into (1) for corresponding value of y

x = 0 : y = 6 - 0 = 6 ⇒ (0, 6 )

x = 5 : y = 6 - 5 = 1 ⇒ (5, 1 )

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Step-by-step explanation:

Summation Notation

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This corresponds with the option:

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3 years ago

Community Gym Charges a $50 membership fee and a $55 monthly fee. Workout Gym charges a $200 membership fee and a $45 monthly fr

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For the Community Gym:
Membership Charge = $50
Monthly fee = $55
So for the 1st month total charge = $(50 +55)
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So after the 2nd month total payment = $(105 + 55)
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After 3rd month total payment = $(160 + 55)
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After 4th month total payment = $(215 + 55)
   = $270
After 5th month total payment = $(270 + 55)
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After 6th month total payment = $(325 + 55)
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Now for the Workout Gym:
Membership Charge = $200
Monthly Charge = $45
So for the 1st month the member pays = $(200 + 45)
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For the 2nd month total payment = $( 245 +45)
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For the 3rd month total payment = $(290 + 45)
   = $335
For the 4th month total payment = $(335 + 45)
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So the 6th month payment in the Community Gym is the same as the 4th month payment in the Workout Gym. The amount will be $380.

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