Solving Systems by 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 the context of solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

What is the solution of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system has infinite solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

Solve for y: 2x + 3y = 6 when x = 2.

Back

y = 0.

Front

Solve for x: 3x + 2 = 11.

Back

x = 3.

Front

If y = 2x + 1, what is the substitution for y in the equation 4x - 3y = 5?

Back

4x - 3(2x + 1) = 5.