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Solving Equations using Elimination help?

I need help with this equation:

Find the point of intersection. Show your work.

3x-2y+2=0

7x-6y+11=0

3 Answers

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  • 9 years ago

    Which would be easiest to eliminate, X or Y? Looks to me that Y would because I can multiply the first equation by 3 and then have two equations with 6y in them. Since they would both have a negative sign I will subtract the second equation from the new first equation:

    9x - 6y + 6 = 0

    7x - 6y +11 = 0

    Subtracting 2nd equation from the first equation gives us 2x - 5 = 0, 2x = 5, x = 2.5

    Substitute for 2.5 in for x in second equation (since you have altered the first equation)

    7(2.5) -6y+6 = 0, 17.5 - 6y +11 = 0 28.5 = 6y y = 4.75

    Now substitute the values for x and y into the original equation to see is everything checks.

    3(2.5) - 2(4.75) + 2 = 0, 7.5 - 9.5 + 2 =0 Check!

  • 9 years ago

    1) 3x-2y+2=0

    2) 7x-6y+11=0

    Multiply 1) by 3

    3) 9x -6y + 6 = 0

    Subtract 3) from 2)

    4) -2x + 5 = 0

    x = 5/2

    Substitute in either 1) or 2) to find y

    Substituting in 1)

    (5/2)*3 - 2y = -2

    15/2 - 2y = - 2

    15 - 4y = -4

    -4y = - 19

    y = 19/4

  • 9 years ago

    3x-2y+2=0

    7x-6y+11=0

    How might you get rid of y? You could multiply the top equation by -3 to make the coefficient in front of y = +6, so when added together y is eliminated.

    (-3)*3x+(-3)*(-2)y+(-3)*2=(-3)*0

    -9x+6y-6=0

    now add:

    7x-6y+11=0

    -9x+6y-6=0

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

    -2x +0y +5 =0

    -2x =-5

    x = 5/2

    Now substitute this back in to either of the original equations:

    3(5/2)-2y+2=0

    3(5/2)-2y+2=0

    15/2 -2y +2 = 0

    19/2 -2y =0

    -2y = -19/2

    y = 19/4

    (5/2, 19/4)

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