Basic Systems of Equations I

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 infinitely many solutions?

Back

It means there are countless sets of values for the variables that satisfy all equations in the system.

Front

How can you determine if a system of equations has a unique solution, no solution, or infinitely many solutions?

Back

By analyzing the equations' graphs: if they intersect at one point, there's a unique solution; if they are parallel, there's no solution; if they are the same line, there are infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) plotted on a coordinate plane.

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

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.