4.2 Systems - Graphing/Elimination/Substitution

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 by substitution?

Back

To solve for one variable in terms of the other and then substitute that expression into another equation.

Front

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

Back

To add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What is the substitution method?

Back

A method for solving systems of equations by expressing one variable in terms of the other.

Front

What is the elimination method?

Back

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

Front

Solve by substitution: y = 5x - 2, -3x + 6y = -12. What is the solution?

Back

(0, -2)