Systems Using Substitution
Key Questions
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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 haven variables.Let us have
3 equations and3 variablesx,y andz . Now pick up an equation withx and segregate it sayx in terms ofy,z . When we put this value ofx in two other equations we get two equations iny andz .We can now find
y in terms ofz say using second equation and when we put in third equation we get value ofz .Once
z is known, it is easy to findy and thenx .