Question

Solve the following system using the Elimination Method; 6x+y=10 and 2x+y=12.

Answers

  1. Hey there!

    The solution to the system is (\frac{1}{2}, 13)

    To solve the system, we can multiply the second equation by -1:

    -2x - y = -12

    Then, we add the two equations together, and solve for x:

    4x = -2

    x = \frac{-1}{2}

    Now, we plug the x value into one of the equations, and solve for y:

    2(\frac{1}{2} ) + y = 12

    -2 + y = 12

    y = 13

    Now we know that the solution to the system is (\frac{1}{2}, 13)

    Hope it helps and have an amazing day!

    Reply

  2. Answer:

    (-1/2, 13)

    Step-by-step explanation:

    Multiply the 2nd equation by -1, obtaining the following system:

    6x + y = 10

    -2x  – y = -12

    ——————

    Combine like terms, obtaining:

    6x + y = 10

    -2x  – y = -12

    ——————

    4x     = -2

    Dividing both sides by 4 yields x = -2/4, or x = -1/2

    Substituting -1/2 for x in the second equation yields:

    2(-1/2) + y = 12, or

    -1 + y = 12.  Then y = 13, and the solution is

    (-1/2, 13)

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