Solving Systems of Equations by Substitution and Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

When is it appropriate to use substitution?

Back

When one equation is easily solvable for one variable.

Front

When is it appropriate to use elimination?

Back

When both equations are in standard form and can be easily manipulated to eliminate a variable.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Solve using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite number of solutions.

Front

Solve using substitution: y = 2x + 1 and 3x - y = 4.

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(1, 3).