System of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the steepness and direction of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.