System of equations

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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

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 infinitely many solutions?

Back

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

Front

How do you find the solution to a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point of intersection.

Front

What is the slope-intercept form of a line?

Back

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

Front

What is the slope of the line represented by the equation y = 3x + 4?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

The solution is (1, 3).