Equations: solving by substitution gives "-2 = 5"

haliebre

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Apr 4, 2006
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Please help:

In solving a system of equations by the substition method, the result of -2=5 is obtained. Which of the following statements is true?

a. The equations are dependent/
b. The solution is (-2,5)
c. There are infintely many solutuions.
d. The system is inconsistent.
 
Re: Equations

Hello, haliebre!

The problem is poorly written . . .

In solving a system of equations by the substition method, the result of 2=5\displaystyle \,-2\,=\,5 is obtained.
Which of the following statements is true?

a. The equations are dependent.
b. The solution is (-2,5)
c. There are infintely many solutuions.
d. The system is inconsistent.

The answer is (d): the system is inconsistent
    \displaystyle \;\;because we arrived at a false statement.

If we get a true statement . . . like 0=0\displaystyle \,0\,=\,0\, or 3=3\displaystyle \,3\,=\,3
    \displaystyle \;\;the system is dependent and has infinitely many solutions.
That is, (a) and (c) are equivalent answers; they gave the same answer twice.
 
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