This question involves solving a simultaneous system of linear equations. The two equations to solve simultaneously are 6x + 8y = 2 and -5x - 16y = 17.
Step 1: You typically start by isolating one variable in one equation. However, to make the calculation easier in this case, let's first simplify these equations by dividing the first equation by 2 and the second equation by -1:
6x/2 + 8y/2 = 2/2 simplifies to 3x + 4y = 1, and -(-5x) - (-16y) = -17 simplifies to 5x + 16y = -17.
Step 2: Now we isolate one of the variables in either equation, in this case let's isolate x in the first equation:
3x = 1 - 4y
==> x = (1 - 4y) / 3
Step 3: Substitute this value of x from the first equation into the second equation:
5[(1 - 4y) / 3] + 16y = -17
==> 5 - 20y + 48y = -51
==> 28y = -56
==> y = -2
Step 4: Substitute y = -2 back into the first equation:
3x + 4(-2) = 1
==> 3x = 1 + 8
==> 3x = 9
==> x = 3
So the solution to the system of equations is x = 3 and y = -2. This means that these values for x and y satisfy both of the original equations.