12/05/24 Solving Systems by Graphing and 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 by graphing?

Back

It involves plotting the equations on a graph and finding the point(s) where they intersect, which represents the solution(s).

Front

What is the elimination method in solving systems of equations?

Back

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

Front

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

Back

If the lines represented by the equations intersect at exactly one point.

Front

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

Back

The lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

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 the system of equations: 7x + 4y = 13 and -7x - 7y = 14.

Back

(7, -9)

Front

Identify the solution to this system of equations: 2x - 3y = -4 and -2x + 7y = -12.

Back

(-8, -4)

Front

How can you tell if two equations are equivalent?

Back

If they simplify to the same equation or represent the same line when graphed.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.