The absolute value of any real number is non-negative. Therefore, for the sum of two absolute values to be equal to zero, both individual absolute values must be equal to zero.
This means that:
x + 12y + 19 = x + 2y - 1 = 0
Solving these two equations simultaneously, we get:
x = -12y - 1 x = -2y + 1
Setting these two expressions equal to each other, we get:
-12y - 19 = -2y + -10y = 2 y = -2
Substitute y = -2 back into one of the equations:
x = -12(-2) - 1 x = 24 - 1 x = 5
Therefore, the solution to the equation |x+12y+19| + |x+2y-1| = 0 is x = 5, y = -2.
The absolute value of any real number is non-negative. Therefore, for the sum of two absolute values to be equal to zero, both individual absolute values must be equal to zero.
This means that:
x + 12y + 19 =
x + 2y - 1 = 0
Solving these two equations simultaneously, we get:
x = -12y - 1
x = -2y + 1
Setting these two expressions equal to each other, we get:
-12y - 19 = -2y +
-10y = 2
y = -2
Substitute y = -2 back into one of the equations:
x = -12(-2) - 1
x = 24 - 1
x = 5
Therefore, the solution to the equation |x+12y+19| + |x+2y-1| = 0 is x = 5, y = -2.