Question

Determine if (−2,4) is a solution to the following system of inequalities.-3x > -7y -37x > -5y -4

Answer 1

Remember that ordered pairs are written in the form (x,y).

Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.

Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.

-3x > -7y - 3

`\begin{gathered} \Rightarrow-3(-2)>-7(4)-3 \\ \Rightarrow6>-28-3 \\ \Rightarrow6>-31 \end{gathered}`

Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).

7x > -5y-4

`\begin{gathered} \Rightarrow7(-2)>-5(4)-4 \\ \Rightarrow-14>-20-4 \\ \Rightarrow-14>-24 \end{gathered}`

Since -14 is greater than -24, then this inequality is satisfied by (-2,4).

Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.