Results 1 to 3 of 3

Math Help - Algebra Help

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    1

    Exclamation Algebra Help

    I just don't understand these last 3 problems. -.-
    Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

    1. How many solutions are there to the following system of equations?
    2x + 5y = -11
    10x + 25y = -55

    Answers:
    a. 0
    b. 1
    c. 2
    d. infinitely many (I think this is the answer?)



    2. How many solutions are there to the following system of equations?
    5x + 3y = 7
    2x - y = 2

    Answers:
    a. 0
    b. 1
    c. 2
    d. infinitely many.


    3. Solve the following system of equations by linear combination:
    2d + e = 8
    d - e = 4

    Answers:
    a. solution is (5,-2)
    b. solution is (4,0)
    c. no solution
    d. infinite number of solutions.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,387
    Thanks
    52
    Quote Originally Posted by LamiaCat View Post
    I just don't understand these last 3 problems. -.-
    Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

    1. How many solutions are there to the following system of equations?
    2x + 5y = -11
    10x + 25y = -55

    Answers:
    a. 0
    b. 1
    c. 2
    d. infinitely many (I think this is the answer?) Yes - multiply eq1 by 5



    2. How many solutions are there to the following system of equations?
    5x + 3y = 7
    2x - y = 2

    Answers:
    a. 0
    b. 1 Solve the second for y and substitute into the first
    c. 2
    d. infinitely many.


    3. Solve the following system of equations by linear combination:
    2d + e = 8
    d - e = 4

    Answers:
    a. solution is (5,-2)
    b. solution is (4,0) Add the two equations together
    c. no solution
    d. infinite number of solutions.
    See above
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by LamiaCat View Post
    I just don't understand these last 3 problems. -.-
    Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

    1. How many solutions are there to the following system of equations?
    2x + 5y = -11
    10x + 25y = -55

    Answers:
    a. 0
    b. 1
    c. 2
    d. infinitely many (I think this is the answer?)
    Hello LamiaCat,

    Notice that the second equation is a multiple of the first. Each term is multiplied by 5. This means they represent the same line and have an infinite number of solutions. We call the system consistent and dependent.


    Quote Originally Posted by LamiaCat View Post
    2. How many solutions are there to the following system of equations?
    5x + 3y = 7
    2x - y = 2

    Answers:
    a. 0
    b. 1
    c. 2
    d. infinitely many.
    Notice that the slopes of the graphs of these equations are not the same. So they are not parallel, nor are they the same line. That only leaves one possibility. They intersect in one point. We call the system consistent and independent.

    Quote Originally Posted by LamiaCat View Post
    3. Solve the following system of equations by linear combination:
    2d + e = 8
    d - e = 4

    Answers:
    a. solution is (5,-2)
    b. solution is (4,0)
    c. no solution
    d. infinite number of solutions.
    Add the two equations together to eliminate e.

    3d = 12
    d = 4

    Substitute back into either equation to find e = 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 4th 2011, 09:39 AM
  2. Replies: 2
    Last Post: December 6th 2010, 04:03 PM
  3. Algebra or Algebra 2 Equation Help Please?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 12th 2010, 12:22 PM
  4. Replies: 0
    Last Post: April 24th 2010, 12:37 AM
  5. algebra 2 help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 4th 2009, 07:24 PM

Search Tags


/mathhelpforum @mathhelpforum