In a system of equations, if one equation is a multiple of another, what can be

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Question: In a system of equations, if one equation is a multiple of another, what can be inferred about their solutions?

Options:

Correct Answer: They have infinitely many solutions.

Solution:

If one equation is a multiple of another, they represent the same line, leading to infinitely many solutions.

In a system of equations, if one equation is a multiple of another, what can be inferred about their solutions?

In a system of equations, if one equation is a multiple of another, what can be inferred about their solutions?

Step 1: Understand what a system of equations is. It is a set of two or more equations with the same variables.
Step 2: Recognize that if one equation is a multiple of another, it means you can multiply the entire equation by a number to get the other equation.
Step 3: Realize that if two equations are multiples of each other, they describe the same line on a graph.
Step 4: Since both equations represent the same line, every point on that line is a solution to both equations.
Step 5: Conclude that there are infinitely many solutions because there are infinitely many points on the line.

Dependent Equations – When one equation is a multiple of another, they represent the same line in a graph, indicating that they have infinitely many solutions.