Me asked in Science & MathematicsMathematics · 1 decade ago

algebra help?

linear combination method

6x + 7y = 26

2x - y = 22

.

4x + 3y = -4

3x + 2y = -1

.

3x - 4y = 14

9x - 12y = 48

.

5x - 8y = 10

6x - 7y = -1

.

6x + 5y = -4

5x - 8y = 21

5 Answers

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  • Mafia
    Lv 4
    1 decade ago
    Favorite Answer

    6x + 7y = 26

    2x - y = 22

    6x + 7y = 26

    7(2x - y = 22)

    6x + 7y = 26

    14x -7y = 154

    20x = 180

    180/20 = x

    9 = x

    plug-in x in one of the original equations and find y.

    Do same with the rest.

  • 1 decade ago

    This method uses the principals of "two equations with two unknowns" and "substitution". So, let's do the first SET;

    Let's use the first equation of 6x + 7y = 26 and solve for x. We subtract 7y from both sides to get 6x = 26 - 7y. Now we divide both sides by 6, and get x = (26 - 7y) / 6. We simplify to x = 26/6 - 7y/6. Now that we KNOW what x is equal to, we can substitute it into the SECOND equation 2x - y = 22, whcih becomes 2(26/6 - 7y/6) - y = 22. Simplify to get 52/6 - 14y/6 - y = 22. Simplify further by subtracting 52/6 from both sides, and you get -14y/6 - y = 22 - 52/6. Now we have all the "y's" on one side...let's get rid of that pesky fraction by multiplying the whole thing through by 6, which gives us -14y - 6y = 132 - 52. Let's combine all the like terms to get -20y = 80. Now solve for y by dividing both sides by -20, and you get y = -4. Now take and plug in y = -4 into the FIRST equation, and solve for x. 6x + 7(-4) = 26, becomes 6x - 28 = 26. Add 28 to both sides to get 6x = 54. Divide both sides by 6, and you get x = 9 ! Now you know what BOTH x and y are equal to.

    Now do the same for each set of equations

    Hope this helps....good luck !

  • 1 decade ago

    6x + 7y = 26

    2x - y = 22

    y=2x-22

    6x+7(2x-22)=26

    6x+14x-154=26

    20x=180

    x=9

    y=2(9)-22

    y=-4

    (9,-4)

    4x + 3y = -4

    3x + 2y = -1

    2y=-1-3x

    y=(-1/2)-(3/2)x

    4x+3((-1/2)-(3/2)x)=-4

    4x-(3/2)-(9/2)x=-4

    (8/2)x-(9/2)x=-(8/2)+(3/2)

    (-1/2)x=(-5/2)

    x=5

    y=(-1/2)-(3/2)(5)

    y=(-1/2)-(15/2)

    y=(-16/2)=-8

    (5,-8)

    Just keep using the same method on each problem

  • Anonymous
    1 decade ago

    6x+7y=26-------------------1

    2x-y=22----------------------2

    Let us multiply equation 2 with 7

    result is

    14x-7y=154----------------------3

    Let us add equation 1 and 3

    Result is 20x=180

    therefore x is 9

    putting x=9 in any equation, we can get the value of y which is -4

    x=9

    y= - 4

    Hope this solve ur problem

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