math

posted by .

How many solutions does the following system have:
2x + 5y = 10
3x + 6y = 12
Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting equation.

  • math -

    The key is to calculate Δ, required for the first part of Kramer's rule.
    Δ=determinant of the left-hand side.

    If Δ≠0, then there is a unique solution, including the trivial solution of x=0 and y=0 if the right-hand side is all zeroes.

    If Δ=0, then the left-hand side of the equations are linearly dependent.
    Two cases may arise:
    1. If the equations are consistent, one single equation will result after reduction of the left-hand side.
    This case has infinitely many solutions, one set for each value we assign to x (or y).
    2. If the equations are not consistent, then after reduction, the equations will be identical on the left-hand side, but the right-hand sides will different.

    This gives a total of 3 different cases.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 2

    I need help with this problem because I do not have a graphing calculator. Explain how you would solve this equation using your graphing calculator in five steps then give the solution. 2x- 3y=8 5x+ 4y= 11 Also how do you determine …
  2. algebra 2

    Classify the system , and determine the number of solutions. This system is inconsistent. It has infinitely many solutions. This system is consistent. It has infinitely many solutions. This system is inconsistent. It has no solutions. …
  3. Algerbra II

    Classify the system , and determine the number of solutions. The system is consistent and dependent and has infinitely many solutions. The system is inconsistent and independent and has no solutions. The system is inconsistent and …
  4. Math - number of solution

    Determine the number of solutions for the system without solving. 3x+12y=-27 4x+2y=34
  5. algebra

    How many solutions does the following system have: 6x - 3y = 9 2x - y = 3 Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting equation. could you please explain …
  6. Algebra 2 Helpp :(

    QUESTIONS (vvv) (1) Solve the system by subsitution 2x + y = -11 3 - 4y = 11 (2) Solve the system by elimination 2x + 6 = -12 5x - 5y = 10 (3) What is the solution of the following system?
  7. math

    Determine the number of solutions for the following system of equations 2x+5y=7 10y=-4x+14 1)Exactly one solution 2)No solutions 3)infinite solutions 4)Exactly 2 solutions I solved the equations and got y=7-2X/5 y=-4X+14/10 and I said …
  8. MAT222

    -x+2y=-2 x-2y=2 the system has no solution the system has a unique solution: the system has infinitely many solutions. they must satisfy the following equation: y= the answer is the system has infinitely many solutions. i just don't …
  9. MAT222

    -x+4y=4 x-4y=-4 the system has no solution the system has a unique solution: the system has infinitely many solutions they must satisfy the following equation: y=0 the answer is the system has many solutions i just don't know the answer …
  10. pre calculus

    Create systems of equations in two variables that have (a) no solution, (b) one distinct solution, and (c) infinite solutions. Show that each system has the indicated number of solutions by using a graph or solving the system.

More Similar Questions