Question $-6 y+18 x=9$

Studdy Solution

STEP 1

What is this asking? We're asked to solve the equation $-6y + 18x = 9$ for $y$ , meaning we want to rewrite the equation so it looks like $y = \text{something}$ . Watch out! Don't forget to keep track of those negative signs!
They can be sneaky.

STEP 2

1. Isolate the term with $y$ .
2. Solve for $y$ .

STEP 3

We're starting with $-6y + 18x = 9$ .
Our goal here is to get $-6y$ by itself.

STEP 4

To get $-6y$ alone, we need to move that $18x$ to the other side.
Since $18x$ is being added to $-6y$ , we'll subtract $18x$ from both sides of the equation: $-6y + 18x - 18x = 9 - 18x$ $-6y = 9 - 18x$ Now, $-6y$ is isolated!

STEP 5

We have $-6y = 9 - 18x$ .
Since we want just $y$ , we need to divide both sides by $-6$ : $\frac{-6y}{-6} = \frac{9 - 18x}{-6}$ Remember, dividing by $-6$ is the same as multiplying by $\frac{1}{-6}$ .

STEP 6

On the left side, $-6$ divided by $-6$ is 1, so we have $1 \cdot y$ , or just $y$ .
Awesome! On the right side, we can distribute the division: $y = \frac{9}{-6} - \frac{18x}{-6}$ Now, let's simplify those fractions.
We have $9$ divided by $-6$ , which simplifies to $-\frac{3}{2}$ .
And $-18x$ divided by $-6$ gives us $3x$ .
So, we get: $y = -\frac{3}{2} + 3x$ We can also write this as: $y = 3x - \frac{3}{2}$ Look at that, we've solved for $y$ !

STEP 7

The solution to the equation $-6y + 18x = 9$ is $y = 3x - \frac{3}{2}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms