System 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 when two equations in a system are parallel?

Back

They have the same slope but different y-intercepts, resulting in no solution.

Front

How do 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 solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane, where the intersection points represent the solutions.

Front

How can you solve a system of equations using substitution?

Back

By 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

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

Front

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

Back

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

Front

How do you solve the system of equations: x + 4y = -3 and x + 7y = -12?

Back

By using substitution or elimination, the solution is (9, -3).

Front

What is the solution to the system of equations: y = 4x + 1 and 3x + 2y = 13?

Back

The solution is (1, 5).