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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations.

Front

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

Back

0 solutions (parallel lines), 1 solution (intersecting lines), or infinitely many solutions (same line).

Front

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

Back

If the equations represent parallel lines that never intersect.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, meaning they are equivalent.

Front

What is substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

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

Back

(3, 0) is the solution.

Front

Solve the system: y = 2x + 3 and 4x - y = 1.

Back

(1, 5) is the solution.