Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What does it mean for a system of equations to have no solution?

Back

It means there are no values for the variables that can satisfy all equations in the system.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means there are an unlimited number of values for the variables that satisfy all equations in the system.

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines representing the equations.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system: y = 2x + 3 and y = -x + 1?

Back

(1, 5)

Front

What is the solution to the system: 3x + 2y = 6 and 6x + 4y = 12?

Back

Infinite solutions.