Math

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How do I solve these problems, I really need help.

Solve by substitution method

6x+5y=17
x=53-8y

Solve by elimination method

2x+3y=5
4x+6y=10

  • Math -

    Substitution method:

    6x+5y=17
    x=53-8y

    Solve for a variable and substitute it in to one of the equations. The easiest way with these two equations is to take x from the second equation and substitute it in to the first equation.

    6(53-8y)+5y = 17

    618 - 48y + 5y = 17
    -48y + 5y = 17 - 618
    -43y = -601
    y = -601/-43

    Then you plug y in to one of the equations and solve for x.

    x = 53 - 8*(601/43)


    Elimination method: The idea is you multiply one equation by a constant so either x or y has the same coefficient as the x or y in the other equation.

    Example:

    #1) x + 3y = 4
    #2) 5x + 2y = -19

    We need to pick a variable to eliminate. The easiest way is to eliminate the x in the second equation. To do this we multiply the first equation by 5 and subtract it from the second.

    5*(x+3y) = 5*4
    5x+15y = 20

    It's tricky to write out the next part online, you normally write the equations directly over each other with a subtraction sign.

    5x + 2y - 5x - 15y = -19 - 20
    -13y = -39

    At this point you can easily solve for y.

    y = -39/-13 = 3

    Then substitute y=3 in to one of the first equations.

    x + 3y = 4
    x + 3*3 = 4
    x + 9 = 4
    x = 4 -9
    x = -5

    --The problem you gave is slightly different.

    2x+3y=5
    4x+6y=10

    In this problem you'd multiply the first equation by 2 and subtract it from the second. The new second equation is then 0 = 0.

    This set of equations is not solvable. Using the elimination method one of the equations is completely eliminated because they are equivalent equations.

  • math -

    how do you do this equation by using elimination.? 8x-5y=11
    4x-3y=5

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