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solve the equation for y

2x + 3y = 6
2x + 3y - 2x = 6 - 2x
3y/3 = -2x + 6/3
y = -2/3x + 2 use properties of equality to isolate y

1 answer

Let's solve the equation step-by-step using properties of equality, starting from the given equation:

  1. Original Equation: \[ 2x + 3y = 6 \]

  2. Isolating the \(3y\) term:
    Subtract \(2x\) from both sides.
    \[ 3y = 6 - 2x \]

  3. Dividing by 3 to solve for \(y\):
    Divide each term by \(3\).
    \[ y = \frac{6 - 2x}{3} \]

  4. Simplifying:
    Split the fraction:
    \[ y = \frac{6}{3} - \frac{2x}{3} \]
    Which simplifies to:
    \[ y = 2 - \frac{2}{3}x \]

You can also write this in slope-intercept form as:
\[ y = -\frac{2}{3}x + 2 \]

Thus, you have successfully isolated \(y\) in the equation:
\[ y = -\frac{2}{3}x + 2 \]