Question12. $5 x-2 y=-10$

Studdy Solution

STEP 1

What is this asking? Rewrite this equation so that $y$ is all by itself on one side of the equals sign. Watch out! Don't forget to keep the equation balanced—whatever you do to one side, you must do to the other!

STEP 2

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

STEP 3

Alright, let's get that $y$ term all by itself!
We've got $5x - 2y = -10$ .
See that $5x$ hanging around with the $y$ ?
Let's move it to the other side.
Since it's a positive $5x$ , we'll subtract $5x$ from both sides to keep things balanced.

STEP 4

$5x - 2y - 5x = -10 - 5x$

STEP 5

That simplifies to $-2y = -10 - 5x$ , which is the same as $-2y = -5x - 10$ .
We're getting closer!
Now, $y$ is almost alone.

STEP 6

We have $-2y = -5x - 10$ .
That $-2$ is stuck to the $y$ through multiplication.
To undo the multiplication, we need to divide.
And remember, what we do to one side, we must do to the other!
So, let's divide both sides by $-2$ .

STEP 7

$\frac{-2y}{-2} = \frac{-5x - 10}{-2}$

STEP 8

This simplifies to: $y = \frac{-5x}{-2} + \frac{-10}{-2}$

STEP 9

So, we have $y = \frac{5}{2}x + 5$ . Boom! We did it!
We've successfully isolated $y$ .

STEP 10

The solution is $y = \frac{5}{2}x + 5$ .

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