We can solve this system of equations by subtracting the second equation from the first:
5x + 3y = 26
-2x + 7y = 6
7x + 4y = 20
Now we can divide both sides by 4 to isolate the y-term:
7x + 4y = 20
4 4 4
7x/4 + y = 5
Now we can subtract 7x/4 from both sides to isolate the x-term:
7x/4 + y = 5
-7x/4 -7x/4
y = 5 - 7x/4
Plugging this back into the first equation and simplifying, we have:
5x + 3(5 - 7x/4) = 26
5x + 15 - 21x/4 = 26
-16x/4 = 11
x = -11/16
Plugging this back into the equation for y, we have:
y = 5 - 7x/4 = 5 - 7(-11/16)/4 = 5 + 33/16
Therefore, the solution to the system is x = -11/16 and y = 33/16.