Bell Work Systems Elimination/Substitution

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 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 simultaneously.

Front

How do you represent a system of equations graphically?

Back

A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Front

What is the purpose of multiplying an equation in the elimination method?

Back

Multiplying an equation is done to create coefficients that will allow for the elimination of one variable when the equations are added or subtracted.

Front

What is the result of eliminating a variable in a system of equations?

Back

Eliminating a variable results in a single equation with one variable, which can be solved easily.

Front

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

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you check your solution after solving a system of equations?

Back

To check your solution, substitute the values of the variables back into the original equations to see if they hold true.