# Video: Changing the Subject of a Formula

The variables 𝑥 and 𝑦 where 𝑥 is non-negative are related by the formula 𝑦 = (6(7 − 𝑥²))/11. Rewrite the formula with 𝑥 as the subject.

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### Video Transcript

The variables 𝑥 and 𝑦, where 𝑥 is non-negative, are related by the formula 𝑦 equals six multiplied by seven minus 𝑥 squared over 11. Rewrite the formula with 𝑥 as the subject.

Now, when we’re looking to rewrite a formula or change the subject of a formula, then what this can involve is a series of inverse operations. Well, first of all, we can see that we’ve got a fraction. So what we want to do is multiply through both sides of the equation by 11. And that’s because if we multiply the right-hand side by 11, what we’re gonna do is remove the denominator. So we’re just gonna be left with the numerator. And whatever we do to one side, we must do to the other.

So therefore, when we do that, we’re gonna get 11𝑦 equals six multiplied by seven minus 𝑥 squared. So then, next, what we can do is divide through by six. And when we do that, we’re gonna be left with 11𝑦 over six equals seven minus 𝑥 squared. So then, it’s gonna be followed by subtracting seven. I’m gonna do that because we want to leave our 𝑥 or 𝑥 squared term on its own. So now, we have 11𝑦 over six minus seven equals negative 𝑥 squared. So we want to have positive 𝑥 squared. So what we need to do now is divide through by negative one. And if we divide through by negative one, what we’re gonna be left with is seven minus 11𝑦 over six is equal to 𝑥 squared.

Well, as we want 𝑥 to be the subject’s formula, not 𝑥 squared, we haven’t quite finished. So what we need to do now is to find a bit of inverse operation. And that is to take the square root because we’ve got 𝑥 squared and we want to do the inverse. We’re gonna take the square root. So when we do that, what we’re gonna get is the square root of seven minus 11𝑦 over six is equal to 𝑥.

So therefore, we can say that the formula rewritten with 𝑥 as the subject is going to be 𝑥 is equal to the square root of seven minus 11𝑦 over six.