Unit 5 - Per 1a

Front

What is a solution in the context of a system of equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the coordinates of the point into each equation. If all equations are satisfied, the point is a solution.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves plotted on a coordinate plane, where the intersection points represent the solutions.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How can you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the significance of the coordinates (x, y) in a solution?

Back

The coordinates represent the values of the variables that satisfy the equations in the system.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines.