CPM Algebra Connections Chapter 6 Review

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What does it mean if a system of equations has 'No Solution'?

Back

A system has 'No Solution' if the equations represent parallel lines that never intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you identify the best method to solve a system of equations?

Back

Consider the form of the equations: use substitution if one variable is isolated, elimination if both are in standard form, and graphing for visual representation.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

Front

How do you set up an equation for substitution?

Back

To set up for substitution, isolate one variable in one equation, then substitute that expression into the other equation.

Front

What does it mean for a system of equations to have 'All Real Numbers' as a solution?

Back

This means that the equations represent the same line, and thus every point on that line is a solution.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the significance of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Front

What is a consistent system of equations?

Back

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