Question

Match each system of linear equations with the correct number of solutions.

A) One solution
B) Infinitely many solutions
C) No solution

Answer 1

A system of linear equations can have one solution, infinitely many solutions, or no solution. The number of solutions can be determined by analyzing the equations.

Step-by-step explanation:

The number of solutions to a system of linear equations can be determined by analyzing the coefficients of the variables and the constants. Here are the possible scenarios:

1. If the system has exactly one solution, it means that the equations intersect at a single point. For example, the equations y = 2x + 3 and y = -x + 5 intersect at the point (2, 7).
2. If the system has infinitely many solutions, it means that the equations are essentially the same line or they overlap. For example, the equations y = 3x + 2 and 2y = 6x + 4 represent the same line.
3. If the system has no solution, it means that the equations are parallel and never intersect. For example, the equations 2x + 3y = 4 and 2x + 3y = 6 are parallel lines.

By examining the equations, you can match them to the correct number of solutions.