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 simultaneously.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

Front

What does it mean if a system of linear equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines represented by the equations coincide, meaning they are the same line.

Front

How can you determine if two lines are parallel from their equations?

Back

If the slopes of the lines are equal and the y-intercepts are different, the lines are parallel.

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method for solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the solution is the point of intersection.

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 convert a linear equation from standard form to slope-intercept form?

Back

Rearrange the equation to solve for y in terms of x.