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 substitution in 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 elimination in 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

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify if both equations are satisfied.

Front

What is the graphical method of solving systems of equations?

Back

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

Front

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

Back

The lines representing the equations 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, meaning every point on the line is a solution.

Front

Solve the system by substitution: 5x + 4y = -14, y = -7x - 15.

Back

(-2, -1)

Front

Solve for x and y: y = 2/3x - 2, y = -x + 3.

Back

(3, 0)