To solve a system of linear equations, you need to find the values of the variables that satisfy both equations simultaneously.
One way to do this is to use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can eliminate either x or y by multiplying one of the equations by a constant that will make the coefficients of x or y equal and opposite in the two equations.
For example, to eliminate y, we can multiply the first equation by 41 and the second equation by 17, giving:
(41)(41x - 17y = 99)
(17)(17x - 41y = 75)
which simplifies to:
1681x - 697y = 4059
289x - 697y = 1275
We can then subtract the second equation from the first:
(1681x - 697y) - (289x - 697y) = 4059 - 1275
which simplifies to:
1392x = 2784
Dividing both sides by 1392 gives:
x = 2
We can now substitute x = 2 into either of the original equations to solve for y. For example, using the first equation:
41(2) - 17y = 99
Simplifying:
82 - 17y = 99
Subtracting 82 from both sides:
-17y = 17
Dividing by -17:
y = -1
So the solution to the system of equations is x = 2, y = -1.