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2 years ago

Solve the system of equations 3x = 84 - 2y 9x = 8y - 24

Mathematics

1 answer:

Eduardwww [97]2 years ago

8 0

Answer:

$3x = 84 - 2y - - - (i) \\ 9x = 8y - 24 - - - - (ii) \\ from \: (ii) \\ 3(3x) = 8y - 24 \\ but \: from \: (i) \: \: 3x = 84 - 2y \\ hence \: put \: (i) \: in \: (ii) \\ 3(84 - 2y) = 8y - 24 \\ 252 - 6y = 8y - 24 \\ 276 = 14y \\ y = \frac{138}{7} \\ x = \frac{104}{7}$

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docker41 [41]

Answer:

There are going to be 31 matches played in the soccer league.

Step-by-step explanation:

The soccer league has 6 teams, so if every team plays against the others twice, there are going to be played 30 matches:

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-Team 2: v Team 3 (2), v Team 4 (2), v Team 5 (2), v Team 6 (2)

-Team 3: v Team 4 (2), v Team 5 (2), v Team 6 (2)

-Team 4: v Team 5 (2), v Team 6 (2)

-Team 5: v Team 6 (2)

-Team 6: -

If there is a final championship game after the 30 regular season matches, there are going to be 31 matches played in the league.

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2 years ago

Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in

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Compound inequality combines multiple single inequalities.

The solution and interpretation of the inequality is:

$x > 50$ and $x < 150$ . Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.

We have:

$110 < 2x + 10$ and $2x + 10< 310$

Solve for x in both inequalities

$110 < 2x + 10$

$110 -10 < 2x$

$100 < 2x$

Divide both sides by 2

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Rewrite as:

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Also, we have:

$2x + 10< 310$

$2x< 310 - 10$

$2x< 300$

Divide by 2

$x < 150$

So, the solutions to the inequalities are:

$x > 50$ and $x < 150$

This means that Ryan needs to consume more than 50 but less than 150 grams of carbohydrates.

Hence, (a) is correct

Read more about compound inequalities at:

brainly.com/question/13290962

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2 years ago

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2 years ago

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