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Flauer [41]
2 years ago
14

Use elimination to solve each system.

Mathematics
1 answer:
Cerrena [4.2K]2 years ago
7 0

Answer:

$3 and $2

Step-by-step explanation:

let p represent popcorn and d drinks , then

2p + 3d = 12 → (1)

3p + 5d = 19 → (2)

multiplying (1) by 3 and (2) by - 2 and adding will eliminate p

6p + 9d = 36 → (3)

- 6p - 10d = - 38 → (4)

add (3) and (4) term by term to eliminate p

0 - d = - 2

- d = - 2 ( multiply both sides by - 1 )

d = 2

substitute d = 2 into either of the 2 equations and solve for p

substituting into (1)

2p + 3(2) = 12

2p + 6 = 12 ( subtract 6 from both sides )

2p = 6 ( divide both sides by 2 )

p = 3

Popcorn costs $3 and a drink costs $2

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Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.
Blizzard [7]

Answer:

The answer is

y = 3

y =  - 4

Step-by-step explanation:

We must find a solution where

\frac{6}{y + 1}  +  \frac{y}{y - 2}  =  \frac{6}{y + 1}  \times  \frac{y}{y - 2}

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

\frac{6}{y + 1}  \times  \frac{y - 2}{y - 2}  +  \frac{y}{y - 2}  \times  \frac{y + 1}{y + 1}

Which equals

\frac{6y - 12}{(y -2) (y + 1)}  +  \frac{ {y}^{2} + y }{(y - 2)(y + 1)}

Add the fractions

\frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)}  =  \frac{6}{y + 1}  \times  \frac{y}{y - 2}

Simplify the right side by multiplying the fraction

\frac{6y}{(y  + 1)(y + 2)}

Set both fractions equal to each other

\frac{6y}{(y + 1)(y - 2)}  =  \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)}

Since the denomiator are equal, we must set the numerator equal to each other

6y =  {y}^{2}  + 7y - 12

=  {y}^{2}  + y - 12

(y  + 4)(y - 3)

y =  - 4

y = 3

6 0
3 years ago
Read 2 more answers
What’s the answer? Because am having a hard time with this math problem.
Studentka2010 [4]

9514 1404 393

Answer:

  34.5 square meters

Step-by-step explanation:

We assume you want to find the area of the shaded region. (The actual question is not visible here.)

The area of the triangle (including the rectangle) is given by the formula ...

  A = 1/2bh

The figure shows the base of the triangle is 11 m, and the height is 1+5+3 = 9 m. So, the triangle area is ...

  A = (1/2)(11 m)(9 m) = 49.5 m^2

The rectangle area is the product of its length and width:

  A = LW

The figure shows the rectangle is 5 m high and 3 m wide, so its area is ...

  A = (5 m)(3 m) = 15 m^2

The shaded area is the difference between the triangle area and the rectangle area:

  shaded area = 49.5 m^2 - 15 m^2 = 34.5 m^2

The shaded region has an area of 34.5 square meters.

7 0
2 years ago
Help help help help please
Gnoma [55]

4Th option is correct ✔️ ✔️

5 0
3 years ago
Read 2 more answers
(picture included) brainliest
Dimas [21]

Step-by-step explanation:

118 is the answer 238-120 = 118

5 0
2 years ago
Claire tried to evaluate 30x8 step by step
Sophie [7]
30x8
8x0=0
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