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 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 first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how do you use substitution?

Back

Substitute 2x + 3 for y in the second equation.

Front

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

Back

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

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

Front

Solve the system by substitution: 2x + y = 10, y = 3x - 2.

Back

(4, -2)

Front

Solve the system by substitution: x + 2y = 8, x = 4 - y.

Back

(4, 2)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.