Question

what is the solution to a system of linear equations?

choose the correct answer below.

a. a value of x
b. an ordered pair that satisfies at least one equation in the system
c. a value of y
d. an ordered pair that satisfies both equations in the system

Explanation:

A system of linear equations (in two variables, typically \(x\) and \(y\)) consists of multiple linear equations. The solution to such a system must satisfy all equations simultaneously (for a consistent system with a unique solution). Option A and C are incorrect because a system's solution isn't just a single \(x\) or \(y\) value (as it involves two variables in typical cases). Option B is incorrect because the solution must satisfy all equations, not just at least one. Option D correctly states that the solution is an ordered pair (representing \(x\) and \(y\) values) that satisfies both equations in the system.

Answer:

D. An ordered pair that satisfies both equations in the system