System 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 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 lines representing the equations coincide, meaning they are the same line.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

Solve the system of equations: 2x + 3y = 12 and x - y = 1.

Back

(3, 2)

Front

Solve the system of equations: 3x + 4y = 10 and 6x + 8y = 20.

Back

Infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

The graph shows the lines of the equations, and their intersections represent the solutions.