Writing and Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has one solution?

Back

It means that the equations represent lines that intersect at exactly one point.

Front

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

Back

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

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and ensure they reflect the problem's conditions.

Front

What is the first step in solving a system of equations by substitution?

Back

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

Front

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

Back

Align the equations and manipulate them to eliminate one variable by addition or subtraction.

Front

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

Back

Substitute the solution back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a coordinate plane, where intersections represent solutions.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.