3x + 2y = 6. Solve for y.
Understand the Problem
The question is asking to solve the equation 3x + 2y = 6 for the variable y. This involves isolating y on one side of the equation to express it in terms of x.
Answer
$$ y = 3 - \frac{3}{2}x $$
Answer for screen readers
The solution for y in terms of x is
$$ y = 3 - \frac{3}{2}x $$
Steps to Solve
- Start with the original equation
We begin with the equation:
$$ 3x + 2y = 6 $$
- Isolate the term with y
To isolate $2y$, we need to move $3x$ to the other side of the equation by subtracting it:
$$ 2y = 6 - 3x $$
- Solve for y
Now, we divide both sides of the equation by 2 to solve for y:
$$ y = \frac{6 - 3x}{2} $$
- Simplify the expression
We can simplify the right side of the equation:
$$ y = 3 - \frac{3}{2}x $$
The solution for y in terms of x is
$$ y = 3 - \frac{3}{2}x $$
More Information
This equation shows that y is a linear function of x, with a slope of $-\frac{3}{2}$ and a y-intercept of 3. The graph of this relationship will be a straight line, indicating how y changes as x changes.
Tips
- Forgetting to move all terms involving x to the other side of the equation when isolating y. Always check that you have correctly moved terms.
- Neglecting to simplify the fractions when solving for y. Make sure to simplify fractions whenever possible.
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