Question

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

Answer 1

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:
\[
y = -\frac{2}{3}x + 2
\]