we know that
If a ordered pair (x,y) is a solution of the equation, then the ordered pair must satisfy the equation
we have the equation
\(7x-5y=28\)
Let's verify all the cases to determine the solution to the problem.
case A) point \((-6,-14)\)
Substitute the values of x and y in the equation
\(x=-6\\y=-14\)
\(7(-6)-5(-14)=28\)
\(-42+70=28\)
\(28=28\) -------> is true
therefore
The point \((-6,-14)\) is a solution of the equation
case B) point \((-1,-7)\)
Substitute the values of x and y in the equation
\(x=-1\\y=-7\)
\(7(-1)-5(-7)=28\)
\(-7+35=28\)
\(28=28\) -------> is true
therefore
The point \((-1,-7)\) is a solution of the equation
case C) point \((4,10)\)
Substitute the values of x and y in the equation
\(x=4\\y=10\)
\(7(4)-5(10)=28\)
\(28-50=28\)
\(-22=28\) -------> is not true
therefore
The point \((4,10)\) is not a solution of the equation
case D) point \((7,9)\)
Substitute the values of x and y in the equation
\(x=7\\y=9\)
\(7(7)-5(9)=28\)
\(49-45=28\)
\(4=28\) -------> is not true
therefore
The point \((7,9)\) is not a solution of the equation
therefore
the answer is
\((-6,-14)\)
\((-1,-7)\)
