The two numbers are 20 and 5
Step-by-step explanation:
let the first number = x
let the second number = y
three times the first number plus seven times the second number equals 95.
3(x) + 7 (y) = 95
3x + 7y = 95 ...(1)
four times the first number minus eleven times the second number equals 25
4(x) - 11(y) = 25
4x - 11y = 25 ...(2)
Combinig both equations:
3x + 7y = 95 ...(1)
4x - 11y = 25 ...(2)
Using elimination method:
multiply equation 1 by 4
multiply equation 2 by 3
The new equations:
12x + 28y = 380 .....(1)
12x - 33y = 75 ........(2)
subtract (2) from (1):
12x - 12x + 28y - (-33y) = 380 - 75
28y + 33y = 305
61y = 305
y = 305/61
y = 5
substitite for y in any of the equation:
Using equation (1): 12x + 28y = 380
12x + 28(5) = 380
12x + 140 = 380
12x = 380 - 140
12x = 240
divide both sides by 12:
x = 240/12
x = 20
The two numbers are 20 and 5