Solve using elimination

-3x - y = -17
-x + y = -7

-3x-y = -17 
-x+y=-1

Using addition 
-4x +0y = -16
-4x=-16
x=4

Then plug the value of x into one of the original equations
-x+y=-7
-(4)+y=-7
y=-7+4
y=-3

The solution is x=4 and y=-3

Thus (4,-3)

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Add the two rows together

−4x=−24
 Solve for x in the above equation
x= 6 

Substitute x=6 into any of the two equations above

Let's pick the first equation -3x-y=-17

−3×6−y=−17
Solve for y in the above equation

y = -1 

Therefore,
x=6
y=-1