SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION

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

How do you determine if a system of equations has no solution?

Back

A system of equations has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

An infinite number of solutions occurs when the equations represent the same line, meaning they have the same slope and y-intercept.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

How can you identify a consistent system of equations?

Back

A consistent system of equations has at least one solution, which can be either a unique solution or infinitely many solutions.

Front

What is the first step in using the elimination method?

Back

The first step is to manipulate the equations, if necessary, to align the coefficients of one variable so that they can be eliminated.

Front

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

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting whether they intersect, are parallel, or are the same line.

Front

How do you solve for a variable after eliminating one variable in a system of equations?

Back

After eliminating one variable, substitute the value of the remaining variable back into one of the original equations to solve for the other variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the point of intersection represents the solution to the system.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in an infinite number of solutions.