solving Systems (elimination, substitution)

Front

What is a system of equations?

Back

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

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable, allowing for the other to be solved.

Front

What is the substitution method?

Back

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

Front

When is the elimination method preferred over substitution?

Back

When the coefficients of one variable are easily manipulated to eliminate that 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 infinitely many solutions?

Back

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

Front

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

Back

(3,0)

Front

Solve by substitution: y = 2x + 1 and 3x + y = 12.

Back

(3,7)