Flashcard 12.06.24 P2

Front

What is the solution to the system: 5x + 4y = -14, y = -7x - 15?

Back

(-2, -1)

Front

What is the solution to the system: 6x + y = -1, y = -3x - 4?

Back

(1, -7)

Front

What is the solution to the system: 4x + 9y = 28, -4x - y = -28?

Back

(7, 0)

Front

What does it mean if a system of equations has 0 solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

Define 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

Define 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 graphical interpretation of a system with one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What is the graphical interpretation of a system with two solutions?

Back

This is not possible for linear equations; they can either intersect at one point, be parallel (0 solutions), or be the same line (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.