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 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 does it mean if a system of equations has infinite solutions?

Back

The equations represent the same line, meaning there are countless points that satisfy both equations.

Front

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

Back

The equations represent parallel lines that never intersect.

Front

How do you solve the system: x = 3y - 13 and 4x + 2y = 4?

Back

Substituting x in the second equation gives the solution (-1, 4).

Front

What is the first step in using substitution to solve a system of equations?

Back

Isolate one variable in one of the equations.

Front

Solve the system: x = -3y - 17 and 2x + 3y = -7.

Back

The solution is (10, -9).

Front

What is the solution to the system: 2x - y = -1 and y = x - 1?

Back

The solution is (-2, -3).

Front

What is the graphical interpretation of a system with one solution?

Back

The lines representing the equations intersect at exactly one point.