3x 6y 0 Calculate Y

This guide explains how to solve the linear equation 3x + 6y = 0 for y. We'll cover the algebraic steps, provide a calculator for quick solutions, and discuss common scenarios where this equation appears.

How to Solve 3x + 6y = 0 for y

The equation 3x + 6y = 0 is a linear equation in two variables. To solve for y, we'll isolate the term containing y on one side of the equation.

Formula Used

Starting with: 3x + 6y = 0

Subtract 3x from both sides: 6y = -3x
Divide both sides by 6: y = -x/2

This shows that y is equal to negative one-half times x. The solution is valid for all real numbers x, meaning there are infinitely many solutions depending on the value of x.

Step-by-Step Solution

Start with the original equation: 3x + 6y = 0
Subtract 3x from both sides: 6y = -3x
Divide both sides by 6: y = -x/2

This final equation shows the relationship between x and y. For any given value of x, you can calculate the corresponding y value.

Worked Example

Let's solve for y when x = 4:

Substitute x = 4 into the equation: 3(4) + 6y = 0 → 12 + 6y = 0
Subtract 12 from both sides: 6y = -12
Divide by 6: y = -2

So when x = 4, y = -2. This confirms our general solution y = -x/2.

Frequently Asked Questions

What does the equation 3x + 6y = 0 represent?: This equation represents a straight line on the Cartesian plane. It shows the relationship between x and y where the sum of 3x and 6y equals zero.
Is there only one solution to this equation?: No, there are infinitely many solutions. For each value of x, there is a corresponding value of y that satisfies the equation.
Can I solve for x instead of y?: Yes, you can rearrange the equation to solve for x: x = -2y. This shows the relationship between x and y from the perspective of x.
What's the slope of the line represented by this equation?: The slope is -1/2, which comes from the coefficient of y in the equation when it's written in slope-intercept form (y = mx + b).