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 for two lines to be parallel in a system of equations?

Back

The slopes of parallel lines are the same.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel and have different y-intercepts.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection of lines on a coordinate plane.

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

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

Back

(3,0) is the solution.

Front

Solve the system: x + y = 5 and x - y = 1.

Back

(3,2) is the solution.