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

Back

It means that the point satisfies all equations in the system.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation and check if both equations are true.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines represented by the equations.

Front

What are the possible types of solutions for a system of equations?

Back

One solution, no solution, or infinitely many solutions.

Front

What does it mean if a system of equations has no solution?

Back

The lines 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, so every point on the line is a solution.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.