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=00=0.

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

    3x+2y= 123x+2y=12
    -6x-4y=246x4y=24

    If you solve this your answer would be 0=00=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=54x8y=5
    -3x+6y=113x+6y=11

    Again, if you solve this your answer would be 0=590=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 nn equations if you have nn variables.

    Let us have 33 equations and 33 variables x,yx,y and zz. Now pick up an equation with xx and segregate it say xx in terms of y,zy,z. When we put this value of xx in two other equations we get two equations in yy and zz.

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

    Once zz is known, it is easy to find yy and then xx.

Questions