4.2 Systems - Graphing/Elimination/Substitution

Front

What are the possible types of solutions for a system of equations?

Back

No solutions, One solution, Infinite solutions.

Front

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

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 lines representing the equations are the same, meaning they overlap completely.

Front

How do you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) of intersection.

Front

What is the solution to the system of equations: y = x and y = -x + 2?

Back

(1, 1)

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the solution to the system of equations: 5x + 3y = 7 and y = 4?

Back

(-1, 4)

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the solution to the system of equations: -2x + y = 1 and 2x + y = 5?

Back

(1, 3)

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.