Answer: (7, 9)
Step-by-step explanation: To solve this system, I would use addition.
To solve a system of equations by addition,
we need one of our variables to cancel out.
Notice that we have a 4x in our first equation.
If we had a -4x in our second equation, the x's would cancel.
To create a -4x in the second equation,
we must multiply the entire equation by -4.
So we have (-4)(x + 6y) = (61)(-4).
Rewriting this equation, we have -4x - 24y = -244.
Now let's rewrite both equations.
4x - 5y = -17
-4x - 24y = -244
_____________
Now when we add the equations together, the x's cancel.
So we're left with -29y = -261.
Now divide both sides by -29 and we have y = 9.
To find x, we plug a y back in for x in either equation.
So let's go with our second equation, x + 6y = 61.
Plugging a 9 in for y, we have x + 6(9) = 61 or x + 54 = 61.
Subtracting 54 from both sides, we have x = 7.
So x = 7 and y = 9 which we can write as the ordered pair (7, 9).