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27 February, 03:16

Solve the system of equations

6x+7y = 5 2x-3y = 7

+1
Answers (1)
  1. 27 February, 03:37
    0
    The solution is (2, - 1)

    Step-by-step explanation:

    * You have two ways to solve the system of equations

    1. Elimination method:

    By making the coefficients of one of the two variables equal in the 2

    equations in magnitude and different in sign to eliminate it and find the

    other variable

    2. Substitution method:

    By finding one of the two variables in terms of the other in one of the

    two equations and substitute this value in the second equation

    * Lets solve our system using the elimination method

    ∵ 6x + 7y = 5 ⇒ (1)

    ∵ 2x - 3y = 7 ⇒ (2)

    - Multiply equation (2) by - 3 to eliminate x

    ∵ (-3) (2x) - (-3) (3y) = (-3) (7)

    ∴ - 6x + 9y = - 21 ⇒ (3)

    - Add equation (1) and (3)

    ∴ 7y + 9y = 5 + - 21

    ∴ 16y = - 16

    - Divide each side by 16

    ∴ y = - 1

    - Substitute the value of y in equation (1)

    ∴ 6x + 7 (-1) = 5

    ∴ 6x - 7 = 5

    - Add 7 to both sides

    ∴ 6x = 12

    - Divide both sides by 6

    ∴ x = 2

    * The solution is (2, - 1)
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