Solutions for Systems 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 for a point to be a solution to a system of equations?

Back

The point satisfies all equations in the system, meaning it makes each equation true when substituted.

Front

How can you determine if a point (x, y) is a solution to a system of equations?

Back

Substitute the x and y values into each equation; if both equations are true, then the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines in a system of equations are parallel?

Back

They have no points in common, meaning there is no solution to the system.

Front

What does it mean if two lines in a system of equations intersect at one point?

Back

There is exactly one solution to the system, which is the point of intersection.

Front

What does it mean if two lines in a system of equations are the same line?

Back

There are infinitely many solutions, as every point on the line is a solution.

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

What is a consistent system of equations?

Back

A system that has at least one solution.