Systems of equations

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 for two lines to be parallel in terms of their slopes?

Back

The slopes of parallel lines are the same.

Front

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

Back

(-3, 4)

Front

How do you solve the system of equations: y = 4x + 1 and 3x + 2y = 13?

Back

Substituting y in the second equation gives the solution (1, 5).

Front

What is the solution to the system: x + 9y = 8 and -6x - 9y = -3?

Back

(-1, 1)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations.

Front

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

Back

It means the lines are parallel and do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.