The answer and steps for this question

Mathematics

2 answers:

Delicious77 [7]3 years ago

7 0

What u do is put the top x equation into the bottom equation. So it would be 5•3y-1-7y=19. Next it would be 15y-7y-1=19. After that it would be 8y-1=19
After you would add 1 to both sides
8y=20
Y=2.5

melamori03 [73]3 years ago

6 0

I will solve your system by substitution.x=3y−1;5x−7y=19Step: Solvex=3y−1for x:Step: Substitute3y−1forxin5x−7y=19:5x−7y=195(3y−1)−7y=198y−5=19(Simplify both sides of the equation)8y−5+5=19+5(Add 5 to both sides)

8y=248y8=248(Divide both sides by 8)y=3Step: Substitute3foryinx=3y−1:x=3y−1x=(3)(3)−1x=8(Simplify both sides of the equation)

x=8 and y=3

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A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium

frosja888 [35]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.

Since a total of 47 hats where purchased, hence:

x + y + z = 47 (1)

Also, he spent a total of $302, hence:

5.5x + 6y + 7z = 302 (2)

He purchases three times as many medium hats as small hats, hence:

y = 3x

-x + 3y = 0 (3)

Represent equations 1, 2 and 3 in matrix form gives:

$\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]$