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?

Back

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

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

How do you solve for y in the equation y = 8x + 1?

Back

The equation is already solved for y; you can substitute values of x to find corresponding y values.

Front

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

Back

(1, 9)

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

Back

(2, 1)

Front

How do you determine if a system of equations is consistent?

Back

A system is consistent if it has at least one solution.

Front

What is the solution to the system: y = 4x + 1 and y = 2x + 5?

Back

(1, 5)

Front

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

Back

(6, 9)