Systems of Equations (Graphing and Substitution)

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 graph a system of equations?

Back

It means to plot the equations on a coordinate plane and find the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

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

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

Solve the system: y = 2x + 1 and 2x + 2y = 20.

Back

x = 3.

Front

Solve the system: y = 8x + 1 and y = 6x + 3.

Back

(1, 9).

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3).

Front

Solve the system: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5).

Front

What is the graphical representation of the solution to a system of equations?

Back

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