Ordered Pairs as Solutions

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a two-dimensional space, written in the form (x, y), where x is the first element (the x-coordinate) and y is the second element (the y-coordinate).

Front

What does it mean for an ordered pair to be a solution of an equation?

Back

An ordered pair (x, y) is a solution of an equation if substituting x for the variable x and y for the variable y in the equation makes the equation true.

Front

How do you determine if (1, 2) is a solution of the equation y = 6x - 4?

Back

Substitute x = 1 into the equation: y = 6(1) - 4 = 2. Since y = 2 matches the ordered pair (1, 2), it is a solution.

Front

How do you determine if (3, 18) is a solution of the equation y = 6x - 4?

Back

Substitute x = 3 into the equation: y = 6(3) - 4 = 14. Since y = 14 does not match the ordered pair (3, 18), it is not a solution.

Front

What is the solution to the equation y = 2x - 7 when x = 2?

Back

Substituting x = 2 gives y = 2(2) - 7 = -3, so the ordered pair (2, -3) is a solution.

Front

Which ordered pair is a solution to the equation y = -5x?

Back

The ordered pair (1, -5) is a solution because substituting x = 1 gives y = -5(1) = -5.

Front

How do you check if (-1, 3) is a solution of y = 4x - 1?

Back

Substituting x = -1 gives y = 4(-1) - 1 = -5. Since y = -5 does not match the ordered pair (-1, 3), it is not a solution.

Front

What is the significance of the x-coordinate in an ordered pair?

Back

The x-coordinate represents the horizontal position of a point on a graph.

Front

What is the significance of the y-coordinate in an ordered pair?

Back

The y-coordinate represents the vertical position of a point on a graph.

Front

What is the graphical representation of an ordered pair?

Back

An ordered pair (x, y) is represented as a point on the Cartesian coordinate plane, where x is the horizontal distance from the origin and y is the vertical distance.