MATH!!!! AHHH!!!

Im studying for finals!

A system of equations is shown below:
8x + 5y = 9 3x + 2y = 4

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this.

Part B: Show that the equivalent system has the same solution as the original system of equations.

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  1. A: let's add them as suggested:

    11x + 7y = 13
    multiply the 2nd by 2
    6x + 4y = 8
    Note: the system : 11x+7y = 13 and 6x + 4y = 8 is not unique, I could have done anything I wanted here.

    B.

    ok, let's solve the original system:
    #1 times 2: 16x + 10y = 18
    #2 times 5: 15x + 10y = 20
    subtract them:
    x = -2
    back in the original #1
    8(-2) + 5y = 9
    5y = 25
    y = 5

    so x = -2, y = 5

    test these in our new system of A
    11x + 7y = 13
    11(-2) + 7(5) = -22 + 35 = 13, Yeah!

    6x + 4y = 8
    6(-2) + 4(5) = -12 + 20 = 8, yeahhhhh!!!!

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  2. Okay so for part A I should put the answer is 6x + 4y = 8 ?

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  3. No,
    you want a "system", which means you need two equations.
    My new system was:
    11x + 7y = 13 and 6x + 4y = 8

    The original 8x + 5y = 9 was replaced by the sum of the two original equations,
    and the original 3x + 2y = 4 was replaced by a multiple of that (I multiplied it by 2)

    I just followed their instructions.

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