Systems Using Substitution

Key Questions

  • Well, I would say that it is easier when you have few equations and variables. If you have 2 equations and 2 variables it is ok; when you get to 3 equations and 3 variables it becomes more complicated, it is still possible, but you have more work to do. The number of substitutions increases together with the possibility to make mistakes.
    More than 3 equations and 3 variables and it gets almost impossible and other methods would be better.

  • For an answer to have an infinite solution, the two equations when you solve will equal 0=0.

    Here is a problem that has an infinite number of solutions.

    3x+2y= 12
    -6x-4y=24

    If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

    For an answer to have no solution both answers would not equal each other.

    Here is a problem that has no solution.

    4x-8y=5
    -3x+6y=11

    Again, if you solve this your answer would be 0=59, this is obviously not true, 0 does not equal 59 so this problem would have no solution.

  • Answer:

    Please see below.

    Explanation:

    I assume you are interested in linear equations. In general you need n equations if you have n variables.

    Let us have 3 equations and 3 variables x,y and z. Now pick up an equation with x and segregate it say x in terms of y,z. When we put this value of x in two other equations we get two equations in y and z.

    We can now find y in terms of z say using second equation and when we put in third equation we get value of z.

    Once z is known, it is easy to find y and then x.

Questions