Solving 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 system of equations to have a solution?

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

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

How can you determine if two equations are equivalent?

Back

If you can manipulate one equation to get the other through algebraic operations.

Front

What is the substitution method for solving systems of equations?

Back

A method where you 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

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method for solving systems of equations?

Back

Plotting both equations on a graph and identifying the point(s) where they intersect.

Front

Solve the system: y = 3x + 2 and y = -x + 4.

Back

(1, 5) is the solution.

Front

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

Back

(3, 0) is the solution.