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Math Help - Substitution equation Problem

  1. #1
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    Substitution equation Problem

    using the substitution method find the solution to each system of equation...
    1.
    2x+3y=7
    6x-y=1

    idk if i got it right but i got y=2.5 and x=1/4 it seems wrong though...
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  2. #2
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    Hello, mathnoobie25!

    Using the substitution method, solve: \begin{array}{cc}(1)\\(2)\end{array}\begin{array}{  cc}2x + 3y \:=\:7 \\ 6x - y\:=\:1\end{array}

    idk if i got it right but i got y=2.5 and x=1/4 it seems wrong though.
    . .
    Don't you know how to check your answers?

    Solve one of the equations for one of its variables.
    . . (Try to choose the easiest one.) *

    Solve equation (2) for y:\;\;y \:=\:6x - 1 (3)

    Substitute into (1): . 2x + 3(6x - 1) \:=\:7

    Solve for x:\;\;2x + 18x - 3\:=\:7\quad\Rightarrow\quad 20x \:=\:10\quad\Rightarrow\quad\boxed{ x \,= \,\frac{1}{2}}

    Substitute into (3): . y \:=\:6\left(\frac{1}{2}\right) - 1\quad\Rightarrow\quad\boxed{ y\,=\,2}

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    Check

    Substitute your answers into the original equations
    . . and see if you get true statements.

    Substitute \left(\frac{1}{2},\,2\right) into (1).
    . . 2\left(\frac{1}{2}\right) + 3(2)\:=\:7 . . . Is this true?
    We have: . 1 + 6 \,=\,7 . . . Yes!

    Substitute \left(\frac{1}{2},\;2\right) into (2).
    . . 6\left(\frac{1}{2}\right) - 2 \,=\,1 . . . Is this true?
    We have: . 3 - 2\,=\,1 . . . Yes!


    Therefore, our answers are correct.


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    *
    We could, say, solve (1) for x:\;\;2x\:=\:7 - 3y\quad\Rightarrow\quad x \:=\:\frac{7}{2} - \frac{3}{2}y

    . . But why introduce fractions when we can avoid them?

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