Solve the system of equations. Start by multiplying the second equation by 2. Then subtract the first equation from the se

Question

Solve the system of equations. Start by
multiplying the second equation by 2.
Then subtract the first equation from the
second.
2x + 4y = 22
13x +2y = 21

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Rylee 2 weeks 2021-09-07T21:02:53+00:00 1 Answer 0

Answers ( )

    0
    2021-09-07T21:03:54+00:00

    The solution to the system of equation is (\frac{5}{6},\frac{61}{12} )

    Explanation:

    Given that the two equations are 2x+4y=22 and 13x+2y=21

    We need to determine the solution to the system of equations.

    It is also given that to start by solving the equations, by multiplying the second equation by 2.

    Thus, we have,

    2(13x+2y=21) \implies 26x+4y=42 ——–(3)

    Let us subtract the first equation from the equation (3), we have,

    -24x=-20

         x=\frac{20}{24}  

         x=\frac{5}{6}

    Thus, the value of x is x=\frac{5}{6}

    Substituting x=\frac{5}{6} in the equation 2x+4y=22 , we have,

    2(\frac{5}{6}) +4y=22

    Simplifying, we have,

    \frac{5}{3} +4y=22

         4y=22-\frac{5}{3}

         4y=\frac{66-5}{3}

         4y=\frac{61}{3}

           y=\frac{61}{12}

    Thus, the value of y is y=\frac{61}{12}

    Hence, the solution to the system of the equation is (\frac{5}{6},\frac{61}{12} )

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