What is the result of adding these two equations? 5x−9y=1 −7x+2y=−5

To add the two equations we just need to combine the like terms on each side of the equation.
Combining the like terms of 5x and −7x gives ${\displaystyle 5x+(-7x)=(5-7)x=-2x}$
Combining the like terms of −9y and 2y gives ${\displaystyle -9y+2y=(-9+2)y=-7y.}$
Combining the like terms of 1 and −5 on the right side of the equation gives ${\displaystyle 1+(-5)=-41+(-5)=-4.}$
Therefore:
${\displaystyle 5x-9y=1}$
${\displaystyle -7x+2y=-5}$
${\displaystyle -2x-7y=-4}$