Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

How do you determine the solution of a system of linear equations graphically?

Back

The solution is the point where the lines intersect on the graph.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What is the graphical representation of the equation 2x - y = 0?

Back

A straight line with a slope of 2 that passes through the origin.

Front

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

Back

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

Front

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

Back

If their slopes are equal and they have different y-intercepts.

Front

What is the solution to the system of equations 4x + 8y = 20 and -4x + 2y = -30?

Back

(7, -1) is the solution.