Answer: x = 4 and 22, y = 4 and 22
The unknown numbers are 4 and 22
Explanation:
Let the two numbers be x and y
If their product is 88, we will have
xy = 88... (1)
If their sum is 26, we will have
x+y = 26... (2)
Solving equation 1 and 2 simultaneously,
From (2), x = 26-y...(3)
Substituting (3) into (1),
(26-y)y = 88
26y - y² = 88
Multiplying through by minus
y²-26y = -88
y² - 26y + 88 = 0
Factorizing this equation,
y² - 22y - 4y + 88 = 0
y(y - 22) -4(y - 22) = 0
(y-4)(y-22) = 0
y = 4 and 22
Substituting the value of y into equation (2) to get x, we have;
x+4 = 26
x = 22
Similarly,
x + 22 = 26
x = 4
Therefore, x = 4 and 22, y = 4 and 22