solve the system of equations using elimination/combinations-2x -y = -4 x + 2y =5

Question

solve the system of equations using elimination/combinations-2x -y = -4 x + 2y =5

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Sophia 3 weeks 2021-09-08T09:26:42+00:00 1 Answer 0

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    2021-09-08T09:28:36+00:00

    Answer:

    x = 1, y = 2

    Step-by-step explanation:

    In the elimination method to solve a system of linear equations, one of the two equations is added/subtracted to the other, in order to eliminate one variable from the equation.

    In this problem, we have the following two equations:

    -2x-y=-4\\x+2y=5

    To solve the system, first we multiply by 2 both sides of the second equation, and we get:

    2(x+2y)=2(5)\\2x+4y=10

    So now the system is

    -2x-y=-4\\2x+4y=10

    Now we add the two equations, and we get:

    (-2x+2x)+(-y+4y)=(-4+10)\\3y=6

    So, we get

    y=\frac{6}{3}=2

    Now we can substitute this value of y into the eq.(2), and we get:

    x+2y=5\\x+2(2)=5\\x+4=5\\x=5-4=1

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