Systems of Equations Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

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

Front

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

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b).

Front

How do you graph a linear equation in slope-intercept form?

Back

Start at the y-intercept (0, b) and use the slope (rise/run) to find another point.

Front

What is the solution to the system of equations represented by the intersection of their graphs?

Back

The solution is the point where the graphs intersect, representing the values of the variables that satisfy both equations.

Front

How do you write an equation from a word problem involving a linear relationship?

Back

Identify the variables, determine the slope and y-intercept, and then write the equation in slope-intercept form.