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 to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations on a graph.

Front

What are the possible types of solutions for a system of linear equations?

Back

No solution, one solution, or infinitely many solutions.

Front

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

Back

The lines representing 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 representing the equations are the same line, overlapping completely.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

Front

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

Back

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

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.