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 is the graphical representation of intersecting lines in a system of equations?

Back

The lines cross at a point, which represents the solution to the system.

Front

What is the substitution method in 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 in 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

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

Back

The solution is the point where the graphs of the equations intersect.

Front

What does it mean for a system of equations to be consistent?

Back

A system that has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system that has no solutions.

Front

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

Back

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

Front

How can you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.