Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

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

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

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

Front

What is a matrix in the context of systems of equations?

Back

A rectangular array of numbers used to represent a system of equations.

Front

How do you represent a system of equations in matrix form?

Back

By creating a coefficient matrix, a variable matrix, and a constant matrix.

Front

What is the first step in solving a system of equations by elimination?

Back

Get both equations in standard form and line up the like terms.

Front

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

Back

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

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.