84.5k views
3 votes
Which of the following statements is true about linear equations of the form ax b=0? A. They always have a unique solution. B. They may have no solution. C. They may have infinitely many solutions. D. They have a solution only if a ≠ 0.

1 Answer

3 votes

Answer:

Explanation:

The expression "ax b=0" may be missing key information. There is no "y" term and, as written, it makes no difference what the value of x is, unless a and b are also variables and not constants. Also, only one equation is given. If a "solution" is to be found, there must be either another equation or condition the information needed to find a "solution."

Let's answer the following question, instead.

Which of the following statements is true about linear equations of the form y = mx + b? and y = m1x + c.

In this case, a solution is the point that both lines intersect (if they do intersect at all). m is the "slope" of the function and b and c are the y-intercepts (the value of y when x is equal to zero).

YES is True. No is False.

A. They always have a unique solution. YES, as long as the slopes (m) are different.

B. They may have no solution. YES, if the slopes (m) are the same and the y-intercepts (b and c) are different. Lines with the same slope are parallel. They have a lot in common, but will never meet.

C. They may have infinitely many solutions. YES, if the slopes (m) and y-intercepts are the same. The lines overlap and so all points are solutions.

D. They have a solution only if a ≠ 0. No. If the slopes are different, they will have a solution. a, the y-intercept6, merely changes the solution.

User Zeroliu
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.