Since the square of any real number is non-negative, the expression can only be equal to 0 when both terms inside the absolute value and the square equal to 0.
So, first, we set 3x - 2y - 4 = 3x = 2y + x = (2/3)y + 4/3
Now, we set 3x - 5y + 3 = 3x = 5y - x = (5/3)y - 1
We have two equations for x, so we can equate them (2/3)y + 4/3 = (5/3)y - 2y + 4 = 5y - 4 + 3 = 5y - 2 7 = 3 y = 7/3
Now we can substitute y back in to find x x = (2/3)(7/3) + 4/ x = 14/9 + 4/ x = (14 + 12) / x = 26 / 9
Therefore, the solution to the equation is x = 26/9, y = 7/3
(3x - 2y - 4)² + |3x - 5y + 3| = 0
Since the square of any real number is non-negative, the expression can only be equal to 0 when both terms inside the absolute value and the square equal to 0.
So, first, we set
3x - 2y - 4 =
3x = 2y +
x = (2/3)y + 4/3
Now, we set
3x - 5y + 3 =
3x = 5y -
x = (5/3)y - 1
We have two equations for x, so we can equate them
(2/3)y + 4/3 = (5/3)y -
2y + 4 = 5y -
4 + 3 = 5y - 2
7 = 3
y = 7/3
Now we can substitute y back in to find x
x = (2/3)(7/3) + 4/
x = 14/9 + 4/
x = (14 + 12) /
x = 26 / 9
Therefore, the solution to the equation is
x = 26/9, y = 7/3