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dusya [7]
3 years ago
5

20 POINTS!!! HELP ME!!!! Use the linear combination method to solve the system of equations. Explain each step of your solution.

3x-8y=7" " " " x+2y=-7
Mathematics
1 answer:
madreJ [45]3 years ago
7 0

The solution of the system of equations is (-3 , -2)

Step-by-step explanation:

Steps for Using Linear Combinations Method)

  • Arrange the equations with like terms in columns
  • Analyze the coefficients of x or y
  • Add the equations and solve for the remaining variable
  • Substitute the value into either equation and solve

∵ 3 x - 8 y = 7 ⇒ (1)

∵ x + 2 y = -7 ⇒ (2)

- Multiply equation (2) by 4 to make the coefficients of y are equal in

 magnitude and different in sign

∴ 4 x + 8 y = -28 ⇒ (3)

Add equations (1) and (3)

∵ 3 x - 8 y = 7 ⇒ (1)

∵ 4 x + 8 y = -28 ⇒ (3)

∴ 7 x = -21

- Divide both sides by 7

∴ x = -3

Substitute the value of x in equation (2) to find y

∵ x + 2 y = -7 ⇒ (2)

∵ x = -3

∴ -3 + 2 y = -7

- Add 3 to both sides

∴ 2 y = -4

- Divide both sides by 2

∴ y = -2

The solution of the system of equations is (-3 , -2)

Learn more:

You can learn more about the system of the linear equations in brainly.com/question/13168205

#LearnwithBrainly

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Marrrta [24]

Answer:

Step-by-step explanation

  1. Let x be the number of adults and y the number of kids

We can then write this two equations :

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  • let's solve the two eaquations

to do that we should combine them both in a way that help us get rid of one of the variables.

             Let's multiply the first equation by -7 to get rid of y by adding it to thr second equation

             -7x-7y= -231

        now add both equations .

              15x+7y-7x-7y=311-231

    we get :  8x = 80

as you notice y is gone and we get a classic easy equation to solve

                x= 80/8

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so the number of adults is 10

let's go back to the first equation ( x+y= 33) and replace x with 10

                10+y= 33

                  y= 33-10

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let's check using the second equation :

            (10*15)+(23*7) = 311

that is true

so :

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