System Of Equations

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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

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

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

Back

The equations represent the same line, meaning they overlap completely.

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 graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the lines intersect on a graph.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What is the solution to the system of equations: 4x - 2y = 8 and 2x - y = 4?

Back

Infinitely many solutions, as the equations are equivalent.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.