Solving Systems of Equations and Absolute Values

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line, regardless of direction.

Front

How do you solve the absolute value equation |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a, then solve for x.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shaped graph that opens upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What methods can be used to solve systems of equations?

Back

Methods to solve systems of equations include graphing, substitution, elimination, and using matrices.

Front

What is an augmented matrix?

Back

An augmented matrix is a matrix that represents a system of equations, including the coefficients and the constants from the equations.

Front

How do you interpret the solution of a system of equations?

Back

The solution of a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

Front

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

Back

A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

Front

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

Back

An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.