Systems 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 for a system of equations to have a unique solution?

Back

It means that the equations intersect at exactly one point, providing one set of values for the variables.

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, resulting in an infinite number of intersection points.

Front

How do you solve a system of equations using the substitution method?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using the elimination method?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection points represent the solutions.

Front

What is the slope of a line in the context of a linear equation?

Back

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

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.