To find the solution to the system of equations ( y = 7x + 2 ) and ( y = 9x - 14 ), set the equations equal to each other: ( 7x + 2 = 9x - 14 ). Solving for ( x ), we get ( 16 = 2x ) or ( x = 8 ). Substituting ( x = 8 ) into either equation gives ( y = 58 ). Thus, the solution is the ordered pair ( (8, 58) ).
When an ordered pair is reflected over the x-axis, the x-value remains unchanged. Only the y-value is altered; it becomes its opposite. For example, if the original ordered pair is (a, b), after reflection, it becomes (a, -b).
Assume we want to find the ordered pair after 90° counterclockwise rotation. From (x,y), we have (-y,x). If we want to find the ordered pair after 90° clockwise rotation, then from (x,y) we have (y, -x)
If the reflection is over the x value, the x-value does not change.
The x coordinate.
The symbol for an ordered pair is (x,y).
To find the solution to the system of equations ( y = 7x + 2 ) and ( y = 9x - 14 ), set the equations equal to each other: ( 7x + 2 = 9x - 14 ). Solving for ( x ), we get ( 16 = 2x ) or ( x = 8 ). Substituting ( x = 8 ) into either equation gives ( y = 58 ). Thus, the solution is the ordered pair ( (8, 58) ).
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(1,2)
When an ordered pair is reflected over the x-axis, the x-value remains unchanged. Only the y-value is altered; it becomes its opposite. For example, if the original ordered pair is (a, b), after reflection, it becomes (a, -b).
Assume we want to find the ordered pair after 90° counterclockwise rotation. From (x,y), we have (-y,x). If we want to find the ordered pair after 90° clockwise rotation, then from (x,y) we have (y, -x)
If the reflection is over the x value, the x-value does not change.
The inverse of an ordered pair (a,b) is the pair (b,a). So you simply switch the order.
The x coordinate.
The second number in an ordered pair (x,y) is the y-coordinate for that point.
The term "ordered" in "ordered pair" signifies that the arrangement of the elements matters. In an ordered pair, like (x, y), the first element (x) is distinct from the second element (y), meaning that (x, y) is not the same as (y, x) unless x equals y. This concept is crucial in mathematics, particularly in coordinate systems, where the position of a point is defined by its x and y coordinates.
A "Cartesian Ordered Pair," more commonly known as simply an "Ordered Pair."