Writing, Substitution, & Elimination

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations using elimination?

Back

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

Front

What is substitution in the context of solving equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

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

Back

Align the equations so that like terms are in the same column, and then manipulate the equations to eliminate one variable.

Front

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

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What is the graphical interpretation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the purpose of rearranging equations before using elimination?

Back

To make it easier to eliminate one variable by aligning coefficients.