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 substitution in the context of systems of equations?

Back

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

Front

How do you isolate a variable in an equation?

Back

Rearranging the equation to get the variable on one side and the constants on the other.

Front

What is the first step in solving the system: y = 3 - x and 3y + x = 5?

Back

Substitute y = 3 - x into the second equation.

Front

What is the solution to the system: y = 3 - x and 3y + x = 5?

Back

(2, 1)

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

Front

What is the solution to the system: y = 8x + 1 and y = 6x + 3?

Back

(1, 9)

Front

What is the best method to solve the system: y = 6x - 11 and -2x - 3y = -7?

Back

Substitution because a variable is isolated.