Determine whether the given ordered pair is a solution of the system of equations? 10 points?

(3, 2);

2x + 3y = 12

x - 4y = -5

Please explain how to solve :)

Thanks, 10 points go to best answer!

6 Answers

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  • 9 years ago

    Just plug in the x and y values into both equations and see if they work. They must

    work in BOTH equations to be a solution.

    (3,2) means x = 3, y = 2 to

    2x + 3y = 12 becomes

    2(3) + 3(2) = 12

    6 + 6 = 12

    12 = 12 so it works for the first one

    x - 4y = -5 becomes

    3 - 4(2) = -5

    3 - 8 = -5

    -5 = -5

    and it works in the 2nd one as well.

    So (3,2) is the solution for the system of equations

    The other way to do this is to find the solution to the system of equations, and see if it turns

    out to be (3,2). You will eventually need to know how to do this anyhow, so here goes.

    Take the 2nd equation

    x - 4y = -5 and add 4y to both sides to make it

    x = 4y - 5 Now you can go to the first equation and "substitute" 4y -5 in place of x

    2x + 3y = 12 becomes

    2(4y-5) + 3y = 12 or

    8y - 10 + 3y = 12 or

    11y - 10 = 12 add 10 to both sides to get

    11y = 22 and divide both side by 11 to get

    y = 2

    since x = 4y - 5 you can plug in y =2 to find x

    x = 4(2) - 5 = 8 - 5 = 3

    so x = 3, y = 2 is the solution

    This is just one of the ways to solve a system of equations, you'll end up learning another

    methods call "elimination" as well.

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  • 9 years ago

    Well 2 lines can only meet at one point so solve the two equations

    2x+3y = 12

    -2(x-4y) = -5

    2x+3y = 12

    -2x+8y = 10

    ------------------------

    11y = 22

    y= 2

    plug y back into any of the two equatons

    2x+3(2)=12

    2x=6

    x=3

    (3,2) is where the two lines intersect so it is a solution

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  • Anonymous
    9 years ago

    Yes they both are.

    Make 2x+3y=12 2*3+3*2=12. Simplify that into 6+6= 12.

    Make x-4y=-5 into 3-4*2=5.4*2 =8 and 3-8=-5.... this is 8th grade math...

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  • JOS J
    Lv 7
    9 years ago

    {x= 3, y= 2}

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  • Bob F
    Lv 7
    9 years ago

    The easiest way is to plug them in

    2(3) + 3(2) = 12, true

    3 - 4(2) = -5, true

    _

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  • 9 years ago

    2x + 3y = 12 ... substitute (3,2) → [ 2(3) + 3(2) = 12 ] ... Okay

    x - 4y = -5 ...... substitute (3,2) → [ (3) - 4(2) = -5 ] ... Okay

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