To find the number bases x and y from the given simultaneous equations, let's solve the system of equations using the method of elimination. The given equations are: 1) 25x - 23y = 10 2) 34x + 32y = 36 To eliminate one of the variables, we can multiply equation 1 by 32 and equation 2 by 23. This will allow us to add the two equations and eliminate the variable y. Multiplying equation 1 by 32: 32 * (25x - 23y) = 32 * 10 800x - 736y = 320 Multiplying equation 2 by 23: 23 * (34x + 32y) = 23 * 36 782x + 736y = 828 Now we can add the two equations: (800x - 736y) + (782x + 736y) = 320 + 828 1582x = 1148 Divide both sides by 1582 to solve for x: x = 1148 / 1582 x ≈ 0.726 Now substitute the value of x into either equation 1 or 2 to solve for y. Let's use equation 1: 25x - 23y = 10 25 * 0.726 - 23y = 10 18.15 - 23y = 10 -23y = 10 - 18.15 -23y = -8.15 Divide both sides by -23 to solve for y: y = -8.15 / -23 y ≈ 0.354 Therefore, the number bases x and y are approximately 0.726 and 0.354, respectively.