Question

determine whether the following statement makes sense or does not make sense, and explain your reasoning. each equation in a system of linear equations has infinitely many ordered - pair solutions. choose the correct answer below. a. the statement makes sense because any equation of the first degree having two variables such as x and y is called a linear equation in two variables and linear equations have an infinite number of solutions. b. the statement does not make sense because any equation of the first degree having two variables such as x and y is called a linear equation in two variables and linear equations have an infinite number of solutions. c. the statement makes sense because any equation of the first degree having two variables such as x and y is called a linear equation in two variables and linear equations have a finite number of solutions. d. the statement does not make sense because any equation of the first degree having two variables such as x and y is called a linear equation in two variables and the linear equations have a finite number of solutions.

Explanation:

To determine if the statement makes sense, we analyze linear equations in two variables. A linear equation in two variables (e.g., \(ax + by = c\), \(a,b\) not both zero) represents a straight line. A straight line has infinitely many points (ordered pairs \((x,y)\)) that satisfy the equation, so each linear equation in two variables has infinitely many solutions.

Now, evaluate the options:

• Option A: Says the statement makes sense and correctly explains that linear equations in two variables (first - degree with two variables) have infinitely many solutions.
• Option B: Says the statement does not make sense but then gives the correct reason (linear equations have infinite solutions) for why it should make sense, so this is contradictory.
• Option C: Says linear equations have a finite number of solutions, which is incorrect.
• Option D: Says linear equations have a finite number of solutions, which is incorrect.

Answer:

A. The statement makes sense because any equation of the first degree having two variables such as x and y is called a linear equation in two variables and linear equations have an infinite number of solutions.