Let's assume the first number is x and the second number is y
we have two equations:
Equation 1: x + y = 29 (The sum of the two numbers is 29)
Equation 2: 4x - y = 6 (The difference between four times the first number and the second number is 6)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 1, we can express x in terms of y:
x = 29 - y
Substituting this value of x into Equation 2:
4(29 - y) - y = 6
Expanding and simplifying:
116 - 4y - y = 6
116 - 5y = 6
Rearranging the equation:
-5y = 6 - 116
-5y = -110
Dividing both sides by -5:
y = -110 / -5
y = 22
Now, substitute the value of y back into Equation 1 to find x:
x + 22 = 29
x = 29 - 22
x = 7
Therefore, the two numbers are 7 and 22.