Unit 8 Flashcard 2

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true.

Front

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

Back

Substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

What is the solution to the system of equations: x + y = 7 and x - y = 3?

Back

The solution is (5, 2).

Front

How can you find the intersection point of two lines represented by equations?

Back

You can solve the equations simultaneously using substitution or elimination methods.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the values of the variables that satisfy all equations in the system.

Front

What does it mean if two equations in a system are identical?

Back

It means that they represent the same line, resulting in infinitely many solutions.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other variable.