Systems of Equations with Elimination and Substitution

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 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

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

Back

A system 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 the solution of a system of equations?

Back

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

Front

Solve the system of equations using substitution: y = 2x + 1 and x + y = 5. What is the solution?

Back

(2, 5)

Front

Solve the system of equations using elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinitely many solutions.

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

What is the first step in the elimination method?

Back

Align the equations and manipulate them to eliminate one variable.