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Use the linear combination method to solve the system of equations. Explain each step of your solution.
3x-8y=7" "
" " x+2y=-7

Respuesta :

Ashraf82

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

Step-by-step explanation:

Let us revise the steps of Linear combinations method

  • Arrange the equations with like terms in columns
  • make the coefficients of x or y equal in magnitudes and different in signs
  • Add the equations and solve for the remaining variable
  • Substitute the value of the variable into one of the two equations to find the second variable

The system of equations is

3 x - 8 y = 7 ⇒ (1)

x + 2 y = -7 ⇒ (2)

Let us make the coefficients of y equal in magnitude by multiplying

equation (2) by 4

∴ 4 x + 8 y = -28 ⇒ (3)

- Add equations (1) and (3) to solve for x

∴ 7 x = -21

- Divide both sides by 7

∴ x = -3

Substitute the value of x in equation (1) to find y

∵ 3(-3) - 8 y = 7

∴ -9 - 8 y = 7

- Add 9 to both sides

∴ -8 y = 16

- Divide both sides by -8

∴ 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/2115716

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