Solving Systems with 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?

Back

Finding the values of the variables that satisfy all equations in the system.

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 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, meaning there are no points that satisfy both equations.

Front

How do you determine if a system has one solution?

Back

If the lines represented by the equations intersect at exactly one point, the system has one solution.

Front

Solve the system: 2x + 3y = 4 and y = 5x - 27.

Back

(5, -2)

Front

Solve the system using substitution: x = 6 and y = 2x - 3.

Back

(6, 9)

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the solution to the system: 3x + 2y = 12 and y = -x + 6?

Back

(0, 6)