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4 January, 21:25

Use the elimination method

1) 3x+y=-1 5x-y=9

2) 4x+6y=24 4x-y=10

3) 2x-y=-3 x+3y=16

4) 2x+3y=7 3x+4y=10

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Answers (1)
  1. 4 January, 23:16
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    1) 3x+y=-1 5x-y=9

    First of all we have add both equation but to be sure that the value we want to eliminate are both in a way that would make it possible t be deleted.

    3x+y=-1

    5x-y = 9

    8x = 8

    x = 1

    In this case we are able to eliminate y becuase if we add + y-y we get that our answer is 0. and 3x + 5x would be 8x and - 1+9 would be equal to 8 and to find x we needed to divided giving us that the answer for x is 1 becuase 8/8 is 1.

    Then to find y we substitude the value of x in any of the formulas.

    3 (1) + y = - 1

    3+y = - 1

    y = - 1-3

    y=-4

    When we have our y value we can determine if it is correct by replace the values.

    5 (1) - - 4 = 9

    5+4 = 9

    9=9

    Up until now we are fine. So we do the same with the other equation.

    3 (1) + - 4=-1

    3+-4=-1

    -1=-1

    So by this we can now detemine that.

    x = 1

    y = - 4

    2) 4x+6y=24 4x-y=10

    4x + 6y = 24

    4x-y=10 (*-1)

    4x+6y=24

    -4x+y=-10

    7y = 14

    y = 14/7

    y = 2

    In this case we are not able to delete any of the variables so we multiplied by - 1 to be able to eliminate x.

    Then to find x we substitute the value of y in any of the formulas.

    4x-2=10

    4x = 10+2

    x = 12/4

    x = 3

    So we now know our variables so we substituted them to see if they are correct.

    4 (3) + 6 (2) = 24

    12+12=24

    24=24

    We do the same with the other equation.

    4 (3) - 2=10

    12-2 = 10

    10 = 10

    So we can assume that.

    x = 3

    y = 2

    3) 2x-y=-3 x+3y=16

    (3*) 2x - y = - 3

    x + 3y = 16

    6x - 3y = - 9

    x+3y = 16

    7x = 7

    x = 1

    In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y.

    Then to find y we substitute the value of x in any of the formulas.

    1 + 3y = 16

    3y = 16-1

    y = 15/3

    y = 5

    So we now know our variables so we substituted them to see if they are correct.

    2 (1) - 5 = - 3

    2-5 = - 3

    -3 = - 3

    We do the same with the other equation.

    1+3 (5) = 16

    1+15=16

    16=16

    So we now are sure that

    x = 1

    y = 5

    4) 2x+3y=7 3x+4y=10

    2x+3y = 7 ( * - 4)

    3x+4y = 10 ( * 3)

    -8x - 12y = - 28

    9x + 12y = 30

    x = 2

    In this case we are not able to delete any of the variables so we multiplied one of teh quations by - 4 to be able to subtract in our sum and the other by 3 to have the same number on y to be able to eliminate y.

    Then to find y we substitute the value of x in any of the formulas.

    2 (2) + 3y = 7

    4+3y=7

    3y = 7-4

    y = 3/3

    y = 1

    So we now know our variables so we substituted them to see if they are correct.

    3 (2) + 4 (1) = 10

    6+4=10

    10=10

    We do the same for the other

    2 (2) + 3 (1) = 7

    4+3 = 7

    7=7

    So with that we can say that.

    x = 2

    y = 1
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