9.1 Intro to Systems 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 represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if two lines intersect at one point?

Back

The system of equations has one unique solution.

Front

How can you determine if two lines are parallel from their equations?

Back

If the slopes of the lines are equal and the y-intercepts are different.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you graph a system of equations?

Back

Plot each equation on the same coordinate plane and look for points of intersection.