Basic Linear Systems Practice

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

A system of equations has one solution when the graphs of the equations intersect at exactly one point.

Front

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

Back

A system of equations has no solution when the graphs of the equations are parallel and never intersect.

Front

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

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve using elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other variable.

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

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How can you determine if two lines are parallel?

Back

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