SOLUTION: Suppose a, b, c and d are constants such that a is not a zero and the system below is consistent for all possible values of f and g. What can you say about the numbers a,b,c and d?

Algebra ->  College  -> Linear Algebra -> SOLUTION: Suppose a, b, c and d are constants such that a is not a zero and the system below is consistent for all possible values of f and g. What can you say about the numbers a,b,c and d?      Log On


   

Question 1191662: Suppose a, b, c and d are constants such that a is not a zero and the system below is consistent for all possible values of f and g. What can you say about the numbers a,b,c and d? Justify your answer.
ax1 + bx2 = f
cx1 + dx2 = g
I am new to this work, so we have not done as many exercises yet, but we are writing a quiz soon, and will appreciate if you can help me solve this question.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

Where @MathLover1 copied/pasted her answer, is this link

https://math.berkeley.edu/~peyam/Math54Su12/Homeworks/RHW1.pdf


You will find the solution there  (Exercise 1.1.28)  in much better format for reading.


Looking at this problem,  I'd say that the condition is equivalent to the statement
that the determinant of the system   (ad - bc)   is not equal to zero.


The particular condition that  a =/= 0  is not relevant,  at all.


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On solving systems of two linear equations in two unknowns by the  Substitution method,
Elimination method,  determinants' method 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
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
in this site.

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.