Systems of Equations using Substitution Practice

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 simultaneously.

Front

What is substitution in the context of solving equations?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The points where the graphs of the equations intersect represent the solutions to the system.

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, meaning every point on the line is a solution.

Front

How do you solve the system of equations: x = 6 and y = 2x - 3?

Back

Substituting x = 6 into y = 2(6) - 3 gives y = 9, so the solution is (6, 9).

Front

How do you solve the system of equations: 5x - 2y = 3 and y = 2x?

Back

Substituting y = 2x into 5x - 2(2x) = 3 gives x = 3, then y = 6, so the solution is (3, 6).

Front

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

Back

Isolate one variable in one of the equations.