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21 March, 22:16

What is the solution tot his system of linear equations 2x + 3y = 3 7x - 3y = 24

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  1. 21 March, 22:42
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    The solution for this system is x = 3 and y = - 1.

    Step-by-step explanation:

    1. Let's solve the system of equations to find out the value of x and y:

    1st equation:

    2x + 3y = 3

    2x = 3 - 3y (Subtracting 3y at both sides)

    x = 3/2 - 3y/2 (Dividing by 2 at both sides)

    2nd equation:

    7x - 3y = 24

    Replacing x with the result of the 1st equation:

    7 (3/2 - 3y/2) - 3y = 24

    21/2 - 21y/2 - 3y = 24

    - 21y/2 - 3y = 24 - 21/2 (Subtracting 21/2 at both sides)

    -21y - 6y = 48 - 21 (Multiplying by 2 at both sides)

    - 27y = 27

    y = - 1 (Dividing by - 27 at both sides)

    Now we can find out the value of x:

    2x + 3y = 3

    2x + 3 (-1) = 3

    2x - 3 = 3

    2x = 6 (Adding 6 at both sides)

    x = 3 (Dividing by 2 at both sides)

    3. Let's prove that x = 3 and y = - 1 are correct in the 2nd equation:

    7x - 3y = 24

    7 (3) - 3 (-1) = 24

    21 + 3 = 24

    24 = 24

    We proved that x = 3 and y = - 1 are correct.
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