Review: Writing & Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

If the lines intersect at exactly one point, the system has one solution.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

Front

How do you solve a system of equations using substitution?

Back

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

Front

How do you solve a system of equations using elimination?

Back

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

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and write them as a system.