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What are two-variable linear equations and how do I solve them?

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  1. 2 June, 09:20
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    A two-variable linear equation system would be something like:

    x+y=240

    2x-y=150

    There are two methods to solve a system like this: substitution and elimination.

    With substitution, one equation is rearranged to find the value of one of the variables and then that variable value is substituted into the equation.

    Rearrange the first equation

    y=240-x

    Substitute the value into the second equation

    2x - (240-x) = 150

    Solve for x.

    2x-240+x=150

    3x-240=150

    3x=390

    x=130

    Lastly, plug in the value found into one of the equations, and solve for the other varaible.

    130+y=240

    y=110

    The second method, elimination, requires the variable terms of the equations to cancel out. In the example given, the y terms will cancel out when added together. However, I will instead match the x terms together to cancel out so show the process.

    Multiply the first equation by - 2

    -2x-2y=-480

    Add the two equations together, combining like terms.

    -2x-2y=-480

    2x-y=150

    0-3y=-330

    Solve for the variable.

    -3y=-330

    3y=330

    y=110

    Lastly, plug the found variable into one of the equations to solve for the other.

    2x-110=150

    2x=260

    x=130

    So, the answer to the equation system x+y=240, 2x-y=150 is (130,110).
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