Algebra problem help on Linear Systems?

Algebra problem help? (Linear Systems)?

-x -3y = 6

3x +y = -4

What is the number of solutions in this system?

A. 0

B. 1

C. Infinitely many

Please show me how you got it, thanks

Comments

  • If you take the two equations one at a time there is many (infinity) solutions coz for a value of "x" there is one value also for "y".

    But since you take those two equations as a system, there is only one solution coz these are equations of lines and lines can meet only on one point (exception if they are one over the other).

    - x - 3y = 6

    -3y = x + 6

    y = -(x+6)/3

    Replace in the second equation :

    3x + y = -4

    3x - (x + 6)/3 = -4

    Smallest common denominator is 3 :

    9x - x - 6 = -12

    8x = -12 + 6

    x = -6 / 8

    x = -3/4

    And for y :

    3*(-3/4) + y = -4

    -9/4 + y = -4

    y = -4 + 9/4

    y = -7/4

    Proof :

    -x - 3y = 6

    3/4 + 21/4 = 6

    24/4 = 6 :ok

    3x + y = -4

    -9/4 - 7/4 = -4

    -16/4 = -4 :ok

    So the answer is B

    where x = -3/4 and y = -7/4

  • right here thake 2x-y=32 and subtract y making it 2x=32+y Then take y-5x=13 and subtract y making it 5x=13-y the y's cancel then you definately upload the relax issues togeather so ur answer would desire to be7x=40 5 then you definately divide so the respond is x=6.40 two then you definately purely pass on from there wish i helped!;-)

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