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 point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Front

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

Back

Substitute the point's coordinates into each equation and check if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines represented by the equations.

Front

What does it mean if two lines in a system of equations are parallel?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines in a system of equations coincide?

Back

They have infinitely many solutions because they are the same line.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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.

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)