Systems of Linear Equations (Two Variables)

Front

What is a solution to a system of linear equations with two variables?

Back

An ordered pair (x, y) that satisfies both equations in the system.

Front

True or False: A solution to a system of two linear equations in two variables must make BOTH equations TRUE.

Back

True

Front

Solve the system of linear equations: x = 8 - 4y and 3x + 5y = 3.

Back

( -4, 3 )

Front

Solve the system of linear equations: y = -4x + 5 and 2x - 3y = 13.

Back

( 2, -3 )

Front

Solve the system of linear equations: 3x - 4y = 14 and 5x + y = 8.

Back

( 2, -2 )

Front

What does it mean for two equations to be consistent?

Back

It means that the equations have at least one solution.

Front

What does it mean for two equations to be inconsistent?

Back

It means that the equations have no solutions.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations.

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.