How do you tell whether the ordered pair (2,5) is a solution to #y2x, y=x+2#?

Question

How do you tell whether the ordered pair (2,5) is a solution to #y>2x, y>=x+2#?

Genesis Allen · Accepted Answer

The point (2,5) satisfies both inequalities so it is a solution

Substitute the values #(x,y)->(2,5)# into each equation.
If each equation is true then (2,5) is a solution.

Ineq1#->y>2x#
Ineq2#->y>=x+2#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider Ineq1")#

#y>2x" "->" "5>2(2)" "->" "5>4" "color(red)(larr" True")#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider Ineq2")#

#y>=x+2" "->" "5>=(2)+2" "->" "5>=4" "color(red)(larr" True") #

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Avery Alexander · Answer

undefined To determine if the ordered pair (2,5) is a solution to the inequalities y > 2x and y ≥ x + 2, substitute the values of x and y into each inequality and check if the resulting statement is true. For the ordered pair (2,5):
1. For the inequality y > 2x:
   - Substitute x = 2 and y = 5: 5 > 2(2) → 5 > 4
   - Since 5 is greater than 4, the inequality is true.
2. For the inequality y ≥ x + 2:
   - Substitute x = 2 and y = 5: 5 ≥ 2 + 2 → 5 ≥ 4
   - Since 5 is greater than or equal to 4, the inequality is true.
Therefore, the ordered pair (2,5) satisfies both inequalities and is indeed a solution.

How do you tell whether the ordered pair (2,5) is a solution to #y&gt;2x, y&gt;=x+2#?

How do you tell whether the ordered pair (2,5) is a solution to #y>2x, y>=x+2#?