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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, so there are countless points of intersection.

Front

How can you determine if two lines are parallel?

Back

If their slopes are equal and their y-intercepts are different.

Front

What is the substitution method for 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 for 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 for x and y: 2x + 3y = 6 and x - y = 1.

Back

(3,0) is the solution.

Front

Solve for x and y: 4x - y = 7 and 2x + y = 3.

Back

(2, -1) is the solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection points of the lines corresponding to the equations.