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 for a system of equations to have a unique solution?

Back

It means the equations intersect at exactly one point.

Front

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

Back

The equations represent parallel lines that never intersect.

Front

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

Back

The equations represent the same line, so they intersect at every point on that line.

Front

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

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What is the graphical method for solving systems of equations?

Back

Graph both equations on the same coordinate plane and identify the point(s) of intersection.

Front

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

Back

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

Front

How do you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.