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Question 1169727: how can you tell without graphing that there is one solution to the system...
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
Answer by ikleyn(52805)  (Show Source):
You can put this solution on YOUR website! .
In Algebra, there are MANY WAYS to solve a system of linear equations and to determine if it has one or more solutions,
or does not have solutions at all.
These methods are Substitution, Elimination, the Determinant method (or Cramer's rule).
The most general criterion for a linear system to have a unique solution is non-vanishing its determinant.
In simple terms, if the determinant of the square coefficient matrix is not zero, then the system has a unique solution .
This general criterion has many modifications.
For example, if a system with two equations in two unknown has UNPROPORTIONAL coefficient lines, then
the determinant is non-zero and the system has a unique solution.
See the lessons
- Solution of the linear system of two equations in two unknowns by the Substitution method
- Solution of the linear system of two equations in two unknowns by the Elimination method
- Solution of the linear system of two equations in two unknowns using determinant
- Geometric interpretation of the linear system of two equations in two unknowns
in this site, and especially the last lesson in this list.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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