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

[haliebre]

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.

 

[soroban]

Re: Equations

Hello, haliebre!

The problem is poorly written . . .

In solving a system of equations by the substition method, the result of \(\displaystyle \,-2\,=\,5\) 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 \(\displaystyle \,0\,=\,0\,\) or \(\displaystyle \,3\,=\,3\)
\(\displaystyle \;\;\)the system is dependent and has infinitely many solutions.
That is, (a) and (c) are equivalent answers; they gave the same answer twice.

 

[haliebre]

Thanks.