Systems of Equations - Substitution

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 by substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you solve the system: x = 7 - 3y and 2x - 3y = -4?

Back

Substituting x into the second equation gives (2(7 - 3y) - 3y = -4), leading to the solution (1, 2).

Front

How do you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by algebraic manipulation, they are equivalent.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

The system has infinite solutions because both equations represent the same line.