The sum of the two integers if they are 5 units apart on the number line, and their product is 126 is -23
System of equations
System of equations are equations that contain unknown variables with more than 1 equation.
Let the required integers be x and y.
If two negative integers are 5 units apart on the number line, then;
x - y = 5
x = 5 + y
If their product is 126, hence:
x y = 126
Substitute
5+y(y) = 126
5y + y^2 = 126
y^2 + 5y - 126 = 0
Factorize
y^2 + 14y - 9y - 126 = 0
y(y + 14) - 9(y + 14) = 0
y = 9 and - 14
Since the integers are negative, hence;
x = 5 + y
x = 5 - 14
x = -9
Sum = -14 + (-9)
sum = -23
Hence the sum of the two integers is -23
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