Systems Elimination (Easy)

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 do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations, where the intersection points represent the solutions.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system: y - 5 = 7x and y - 17 = x?

Back

(2,19)

Front

What is the solution to the system: x + y = 8 and -x - y = 4?

Back

No solution.