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19 May, 07:39

4x + 6y = 12 and 2x + 3y = 6 What is the relationship, if any, between the two equations? Does the system of equations have one solution, no solution, or in finitely many solutions? explain. how can u verify your answers to the two questions above by solving algebraically?

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  1. 19 May, 08:10
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    Step-by-step explanation:

    4x + 6y = 12 ... equation 1

    2x + 3y = 6 ... equation 2

    from equation 2

    2x + 3y = 6 ... equation 2

    2x = 6-3y

    divide both sides by 2

    2x/2 = (6-3y) / 2

    x = (6-3y) / 2 ... equation 3 ... this is the relationship between the two equation.

    substitute for x in equation 1

    4x + 6y = 12 ... equation 1

    4 (6-3y) / 2 = 12

    2 (6-3y) = 12

    12 - 6y = 12

    12-12 = 6y

    0=6y

    divide both sides by 6

    0/6 = 6y/6

    y = 0

    put y=0 in equation 3

    x = (6-3y) / 2

    x = 6-3 (0) / 2

    x = 6-0/2

    x = 6/2

    x = 3.

    when one side of the equation is identical to the other side of the equation, then it is said to have an infinite form of solutions. that is x=x

    so to check if the eqation is infinite, we check by inserting the values of x and y into the equation.

    x = (6-3y) / 2

    3 = 6-3 (0) / 2

    3 = 6-0/2

    3 = 6/2

    3=3

    since 3=3 then the solution is infinite.

    inorder to verify your answer algebracally is by putting the value of x and y in the question to check

    from equation 1

    4x + 6y = 12

    note, y=0, x = 3

    4 (3) + 6 (0) = 12

    12 + 0 = 12

    12=12 ... proved
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