The sum of 2 numbers is 19 and their product is 88?
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To solve this problem, we'll use algebraic equations. Let's assume the two numbers are x and y.
We know that the sum of the two numbers is 19, so we can write the equation:
x + y = 19 (Equation 1)
We also know that their product is 88, which can be expressed as:
xy = 88 (Equation 2)
Now, we can solve this system of equations by substitution or elimination.
Let's solve using substitution. From Equation 1, we can express x in terms of y:
x = 19 - y
Substitute this value of x into Equation 2:
(19 - y)y = 88
Expand the equation:
19y - y^2 = 88
Rearrange to form a quadratic equation:
y^2 - 19y + 88 = 0
Now we can solve this quadratic equation. Factoring or using the quadratic formula, we find that:
(y - 11)(y - 8) = 0
This gives us two possible values for y: y = 11 or y = 8.
Substitute these values back into Equation 1 to find the corresponding x-values:
When y = 11, x = 19 - 11 = 8
When y = 8, x = 19 - 8 = 11
Therefore, the two numbers are 8 and 11.