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guapka [62]
3 years ago
11

Solve the system of equations:

Mathematics
1 answer:
Sophie [7]3 years ago
3 0

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

  • Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
  • Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

<em>I hope this explanation help you</em>

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

#LearnwithBrainly

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Kiran walked at a constant speed. He walked 1 mile in 15 minutes. Which of these equations represents the distance d (in miles)
galben [10]

Answer: d=\dfrac{t}{15}, where d= distance that Kiran walks in t minutes.

Step-by-step explanation:

Given: Kiran walked at a constant speed.

He walked 1 mile in 15 minutes.

The, distance walked by Kiran in 1 minute = \dfrac1{15} mile

The distance that Kiran walks in t minutes = t\times\dfrac{1}{15} miles

If d= distance that Kiran walks in t minutes

The required equation: d=\dfrac{t}{15}

5 0
3 years ago
Serafina had 30 stickers. She gave the same number of stickers to each of her 3 friends. Now she has 18 stickers left. How many
worty [1.4K]

Answer:

4 stickers were given to her three friends

Step-by-step explanation:

30 -18=12

12 sticker were distributed to safrina's 3 friends

so, 12÷3 =4

5 0
2 years ago
Rema purchased 18 ounces of gold in 2005 for $414 per ounce in order to try to diversify her investment portfolio. She sold a th
Licemer1 [7]

Given :

Rema purchased 18 ounces of gold in 2005 for $414 per ounce in order to try to diversify her investment portfolio.

She sold a third of her holdings in gold in 2009 at a price $953 per ounce. She sold the rest of her gold holdings in 2010 for $1,367 per ounce.

To Find :

What is Prema’s profit in 2009 and 2010.

Solution :

Price of one third ounces of gold, in 2005 is :

P = $414/3 = $138 .

Profit from selling them in 2009 is :

P1 = $(953 - 138) = $815 .

Profit from selling them in 2010 is :

P2 = $( 1367 - ( 414 - 138 ) ) = $1091 .

Therefore, Prema's profit in 2009 is $815 and 2010 is $1091.

Hence, this is the required solution.

5 0
2 years ago
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Paul [167]

Answer:

{x}^{2}  + 2x + 1

Step-by-step explanation:

They ask: f(x) - g(x) =

( {x}^{2}  + 3x + 2) - (x + 1)

{x}^{2}  + 2x + 1

5 0
3 years ago
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nydimaria [60]

Answer:

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Step-by-step explanation:

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So since we need 4 pizza slices to be gone in order to make 1/2 of the pizza...

and since we know that there are three slices missing....

the equation for this is 8-3=5 and we can't have 5 we need 4 so we need 1 more slice to be eaten

6 0
3 years ago
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