You can perform such operations by which y gets on one side and rest of the stuffs get on other side of the equation.
The expression for y for given case is
[tex]y = 2x + 3[/tex]
Since the given equation is
[tex]9x + 18 = 6y - 3x[/tex]
Thus, we see that if we could remove that -3x and 6 from the right side, the variable y would become free and the other side of the equation will express its value expression.
For that, we will add 3x first to the given equation on both the sides so that equation doesn't get changed(function type operations on both sides of an equation do not alter the equality)
Thus,
[tex]9x + 18 = 6y - 3x\\\text{Adding 3x on both sides}\\\\9x + 18 + 3x = 6y - 3x + 3x \\(9+3)x+ 18 = 6y + 0 = 6y \text{\: (It is because like terms' addition gets applied on coefficients)}\\12x + 18 = 6y[/tex]
Dividing both sides of the equation with 6, we get:
[tex]\dfrac{12}{6}x + \dfrac{18}{6} = \dfrac{6}{6}y\\\\2x+3 = y \text{\:\:(1 is genereally not written in coefficient as it is already present as factor)}\\\\y = 2x + 3[/tex]
Thus,
The expression for y for given case is
[tex]y = 2x + 3[/tex]
Learn more about finding value of variables here;
https://brainly.com/question/8564982
