Question

For each ordered pair (x,y) determine whether it is a solution to the inequality 7x+2y>_26

Answer 1

The inequality is given as,

`7x+2y>-26`

Consider that any ordered pair (x,y) is said to be the solution of the inequality if the ordered pair gives a true result when substituted in the inequality.

Consider the ordered pair (4,-9),

`\begin{gathered} 7(4)+2(-9)>-26 \\ 28-18>-26 \\ 10>-26 \end{gathered}`

Clearly, the result is true. So it can be concluded that (4,-9) is a solution of the given inequality.

Therefore, mark YES for the ordered pair (4,-9).

Consider the ordered pair (3,4),

`\begin{gathered} 7(3)+2(4)>-26 \\ 21+8>-26 \\ 29>-26 \end{gathered}`

Clearly, the result is true. So it can be concluded that (3,4) is a solution of the given inequality.

Therefore, mark YES for the ordered pair (3,4).

Consider the ordered pair (-4,0),

`\begin{gathered} 7(-4)+2(0)>-26 \\ -28+0>-26 \\ -28>-26 \end{gathered}`

Clearly, the result is false as -28 is not actually greater than -26.

So it can be concluded that the ordered pair (-4,0) is not a solution of the given inequality.

Therefore, mark NO for the ordered pair (-4,0).

Consider the last ordered pair (-6,8),

`\begin{gathered} 7(-6)+2(8)>-26 \\ -42+16>-26 \\ -26>-26 \end{gathered}`

Note that the numbers on both sides of the inequality are identical. So there should be the symbol of equality, not inequality. So, it can be concluded that this ordered pair (-6,8) is not a solution of the given inequality.

Therefore, mark NO for the ordered pair (-6,8).