Solving Systems by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system by elimination?

Back

Solving a system by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by removing one variable, allowing for the solution of the remaining variable.

Front

How do you determine which variable to eliminate?

Back

Choose the variable that can be easily eliminated by adding or subtracting the equations, often based on their coefficients.

Front

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

Back

The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

Front

What does it mean if a system has no solution?

Back

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

Front

What does it mean if a system has infinite solutions?

Back

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

Front

What is a unique solution in a system of equations?

Back

A unique solution occurs when the equations intersect at exactly one point, providing specific values for the variables.

Front

How can you check your solution for a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by each equation on a coordinate plane.