we will proceed to verify each case to determine the solution of the problem
we know that
If the ordered pair is a solution of the inequality , then the ordered pair must be satisfied the inequality
we have
\(y-3x < -4\)
case A point \((4,-2)\)
Substitute the values of x and y in the inequality
\(-2-3*4 < -4\)
\(-14 < -4\) -------> is true
therefore
the pair ordered \((4,-2)\) is a solution of the inequality
case B point \((0,-3)\)
Substitute the values of x and y in the inequality
\(-3-3*0 < -4\)
\(-3 < -4\) -------> is false
therefore
the pair ordered \((0,-3)\) is not a solution of the inequality
case C point \((5,1)\)
Substitute the values of x and y in the inequality
\(1-3*5 < -4\)
\(-14 < -4\) -------> is true
therefore
the pair ordered \((5,1)\) is a solution of the inequality
case D point \((-3,0)\)
Substitute the values of x and y in the inequality
\(0-3*(-3) < -4\)
\(9 < -4\) -------> is false
therefore
the pair ordered \((-3,0)\) is not a solution of the inequality
case E point \((1,-1)\)
Substitute the values of x and y in the inequality
\(-1-3*(1) < -4\)
\(-4 < -4\) -------> is false
therefore
the pair ordered \((1,-1)\) is not a solution of the inequality
therefore
the answer is
\((4,-2)\)
\((5,1)\)
