System of Equations (solutions, graphing, and substitution)

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines coincide, or are the same line.

Front

How do you graph a system of equations?

Back

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

Front

What is substitution in solving systems of equations?

Back

It is a method where you solve one equation for a variable and substitute that value into the other equation.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

How do you find the slope from an equation in slope-intercept form?

Back

The slope is the coefficient of x in the equation y = mx + b.

Front

What is the y-intercept of a line?

Back

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

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

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