How do I solve the equations 2x + 13y = 4 and x + 8y = 9?

x = 9 - 8y

Now we substitute this expression for x into the first equation:

2(9 - 8y) + 13y = 4

Expanding this gives:

18 - 16y + 13y = 4

Combine like terms:

18 - 3y = 4

Now, solve for y:

-3y = 4 - 18
 -3y = -14
 y = 14/3

Next, we substitute y back into the equation we derived for x:

x = 9 - 8(14/3)

Calculating this we have:

x = 9 - 112/3
 x = 27/3 - 112/3
 x = -85/3

Thus, the solution to the system of equations is:

x = -85/3, y = 14/3

Both values can be expressed as decimals if needed, but this is the solution in fraction form which is often preferred in mathematics. This method allows us to find the values of x and y that satisfy both equations simultaneously.