\[\begin{aligned}
& 9x+4y<8
\\\\
& -3x-7y\geq 5
\end{aligned}\]
Is
\[(1,-2)\] a solution of the system?
To check if the point (1,-2) is a solution of the system, we substitute the values of x and y into each equation and see if the inequalities are satisfied.
For the first equation:
\[9x+4y<8\]
Substituting x=1 and y=-2, we get:
\[9(1)+4(-2)<8\]
\[9-8<8\]
\[1<8\]
The inequality is satisfied.
For the second equation:
\[-3x-7y\geq 5\]
Substituting x=1 and y=-2, we get:
\[-3(1)-7(-2)\geq 5\]
\[-3+14\geq 5\]
\[11\geq 5\]
The inequality is satisfied.
Since both inequalities are satisfied when we substitute x=1 and y=-2, we can conclude that (1,-2) is a solution of the system.