Systems of Equations (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 the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

When is substitution the best method to use?

Back

When one variable is isolated or can be easily isolated.

Front

What is an isolated variable?

Back

A variable that is expressed alone on one side of an equation.

Front

How do you solve the system: y = 2x + 3 and x + y = 10?

Back

Substituting y in the second equation gives x + (2x + 3) = 10, leading to x = 7, y = 17.

Front

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

Back

The lines representing the equations intersect at exactly one point.

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 infinite solutions?

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.