Substution Soluton MATH

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1. y= -5x+2
y=3x-14

2. x+y=0
5x+y=4

3. 6x+2y=4
4x+2=8

  • Substution Soluton MATH -

    1. subtituting we get -5x + 2 = 3x-14

    so we get 8x = 16 and x=2, then plugging back in we get y = 2*-5 + 2 = -8

    2. subtracting first from second equation gives us 4x = 4 so x = 1, and y = -1

    3. 4x + 2 = 8 so 4x = 6, and x = 3/2
    also thus 3/2*6 + 2y = 4
    2y= -5
    y = -5/2

    maybe you had a typo and meant the second equation is 4x+2y = 8

    so then we subtract frist equation from second one and get 2x = -2, x=-1
    then we plug back in for the second one to get -4 + 2y = 8
    y= 12/2 = 6

    :D

  • Substution Soluton MATH -

    1. since we have two expressions each equal to y, just equate them:
    3x-14 = -5x+2
    8x = 16
    x=2
    sub into one of them:
    y = 3x-14 = 6-14 = -8

    2. from the first : y = -x
    into the 2nd:
    5x -x = 4
    4x=4
    x = 1
    then y = -1

    3. probably a typo , you meant: 4x + 2y = 8

    6x+2y=4
    4x+2y=8
    subtract them:
    2x = -4
    x = -2
    into 4x+2y=8 ---> -8+2y=8
    2y = 16
    y = 8

  • Substution Soluton MATH -

    Reiny I don't understand the second part of number 3. Please explain. Actually I really didn't understand the whole thing. Why did you subtract the two equations? than when you got the answer for x I don't even know what happened after that

  • Substution Soluton MATH -

    3. Assuming it was a typo and the 2nd equation was 4x+2y = 8,

    notice that both terms contain 2y as the y-term.
    The method I used is called "elimination".

    if we subtract the two equations, of course we can only add/subtract like terms, I get:
    6x-4x = 2x
    2y - 2y = 0 ----> Ahh, I have "eliminated" the y term
    4-8 = -4
    giving me
    2x + 0 = -4
    2x = -4
    x = -2

    now go back to either of the original equations, I picked the 2nd
    4x+2y = 8
    4(-2) + 2y = 8
    -8 + 2y = 8
    2y = 16
    y = 8

    You should try substituting x=-2 into the first, to see that you get the same answer for y.
    I usually pick the easier-looking equation.

    after becoming a bit more proficient in your algebra, some of those last steps can be skipped.

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