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 involves plotting the equations on a coordinate plane to find their intersection point(s), which represent the solution(s) of the system.

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

Front

Solve the system: y = 2x + 1 and y = -x + 4. What is the solution?

Back

(1, 3)

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.

Front

How can you check your solution to a system of equations?

Back

By substituting the solution back into both original equations to see if they hold true.

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

Solve: 3x + 2y = 6 and y = 3 - x. What is the solution?

Back

(0, 3)