X - y= 4 , 2x + y= 5 solve linear equations and express in ordered pairs?

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Is system independent, inconsistent or dependent? Please show algebraic steps used to get this answer.
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  • s k answered 6 years ago
To find the ordered pair, you use either substitution or you can combine the equations. I think substitution's more fun, so I'll do that.

x-y=4 -> y=x-4
2x+y=5 -> 2x+x-4=5 -> 3x=9 -> x=3
y=x-4 -> y=3-4 -> y=-1

The ordered pair is, therefore, (3,-1). You can check this if you want by plugging the numbers back into the original equations.

Because the lines for y=x-4 and y=5-2x are not parallel and intersect at one point, the system is independent.

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5 out of 5
Simplistic breakdown- great teaching mechanism!
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  • mohamed f answered 6 years ago
    when x-y=4
    And 2x+y=5

    x=4+y
    then 2( 4+y ) + y=5
    8+2y+y=5 & 3y=5-8 then 3y=-3
    Y = -1
    x - ( -1 ) =4 & x+1=4
    X = 3
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  • Wile E. answered 6 years ago
    x - y = 4
    2x + y = 5
    ¯¯¯¯¯¯¯¯¯¯¯
    - x = - 1 (Subtract second equation from first)
    x = 1

    1 - y = 4 (Substitute 1 for y)
    - y = 4 - 1
    - y = 3
    y = - 3

    Ordered Pair (1, - 3)
    ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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  • angella answered 6 years ago
    x=3 y= -1

    independent

    1x - 1y = 4
    2x + 1y = 5
    -------------------
    3x + 0y = 9

    x = 3
    y=-1
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  • grizabeLLa's offspring answered 6 years ago
    2x+y=5 ; x-y=4
    2(3)+(-1)=5 (3)-(-1)=4
    6-1=5 3+1=4

    x=3 ; y= -1

    not sure. XD

    Source(s):

    http://www.algebra.com/algebra/homework/coordinate/lessons/Types-of-systems-inconsistent-dependent-independent.lesson
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  • mathman241 answered 6 years ago
    x=3 y= -1

    independent

    1x - 1y = 4
    2x + 1y = 5
    -------------------
    3x + 0y = 9

    x = 3
    y=-1
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  • shinsplints99 answered 6 years ago
    x - y = 4 (EQ1)
    2x + y = 5 (EQ2)

    Solve EQ1 for x:
    x = y + 4

    Substitute this value into EQ2:
    2(y + 4) + y = 5

    Solve for y:
    2y + 8 + y = 5

    3y = -3

    y = -1

    Plug into EQ1 and solve for x:
    x - (-1) = 4

    x + 1 = 4

    x = 3

    Solution:
    (3, -1)
    Dependent
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