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Math Help - Need help with solving systems of equations

  1. #1
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    Exclamation Need help with solving systems of equations

    Hey! So I'm completely lost on figuring out how to solve system of equations. I'm researched it everywhere and I just can't seem to figure out how to do this. Here are some specific questions I need help with.

    Solve the system of equations using the graphing method. What does the graph look like?
    y = x
    y = (-2/3)x + 5

    a) 2 lines intersecting at (3,3)
    b) 2 lines intersecting at (-3,-3)
    c) 2 lines intersecting at (2,2)
    d) 2 lines intersecting at (-2,-2)


    Solve this system of equations:

    x = 2y - 8
    4x + y = 13

    a) (2,-5)
    b) (-2,5)
    c) (2,5)
    d) (-2,-5)

    What is the correct first step to solve this system of equations?
    4x - 3y = -10
    2x + 3y = 4

    a) add the 2 equations together
    b) subtract the 2 equations
    c) multiply the second equation by 3
    d) divide the first equation by 4



    I'd really appreciate if someone could explain to me how to do these problems and how to solve system of equations in general. Thanks so much!
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  2. #2
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    Re: Need help with solving systems of equations

    Hey rachelephilipp.

    When you want to find an intersection between objects, all you are doing is finding where both of them are equal. If you get a contradiction of some sort (like 2 = 3 or 0 = 1), then it means there is no intersection, but if you get a value that makes sense (like x = 3, or y = 7) then that is where both objects meet.

    So to get you started off lets look at the first scenario.

    We have y = x and y = (-2/3)x + 5. If these two intersection it means they both must be equal and have the same x and y values and if this is the case then y = y for bot expressions which means we have x = (-2/3)x + 5 since an intersection means that both y's and x's are going to be equal for the intersected point.

    So based on this, can you now solve for your unknown x value and get the remaining y value to get the point of intersection?
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  3. #3
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    Re: Need help with solving systems of equations

    For the 1st part, do you know how to graph a line? If yes, then carefully graph those two lines and look at where they intersect (cross each other). Give your best guess for the coordinates of that point where they intersect.

    There are several methods to solve a system of equations. You can operate on entire equations, "adding the equations together" (which amounts to adding equals to equals to produce equals, so is acceptable), or algebraically manipulate one to solve for just one variable, then substitute that into the other equation. No matter how it's done, the goal is to produce equations containing just one unknown - because those you can solve using the techniques of Algebra1.

    If you're finding it confusing, I think it's best to learn the "solve for one in terms of the others, then substitute" method first.

    EX:
    x+y = 5
    -5x -3y = -11
    1st, take the first equation and solve for x (in terms of y): x = 5-y.
    Next, substitute that expression for x into the other equation:
    -5x -3y = -11
    so -5(5-y) -3y = -11.
    Now solve it as an Algebra 1 problem:
    (-25 + 5y) - 3y = -11, so -25 + 5y - 3y = -11, so 2y - 25 = -11, so 2y = 25-11 = 14, so y = 7.
    Finally, since have found the value of y, plug it into the first equation to find the value of x:
    x+y = 5, so x+(7) = 5, so x = -2.
    Solution is y=7, x = -2.
    Check:
    x+y = 5 becomes (-2) + (7) = 5. Yup.
    -5x -3y = -11 becomes -5(-2) -3(7) = 10 - 21 = -11. Yup.
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