Solving Systems with Substitution

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 the solution to the system 2x + 3y = 4 and y = 5x - 27?

Back

(5, -2)

Front

How many solutions can a system of equations have?

Back

A system can have one solution, no solution, or infinitely many solutions.

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, so every point on the line 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 is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution.

Front

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

Back

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