Making x the subject in two equations

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  • Thread starter Ellie1
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In summary, to make x the subject in these equations, we must isolate it on one side of the equation by performing inverse operations. In the first equation, we divide both sides by 2 and then take the square root of both sides, while also considering the condition that y must be greater than or equal to 3. In the second equation, we simply divide both sides by the square root of 3.
  • #1
Ellie1
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how do you make x the subject in
\(\displaystyle y=2x^2 +3\)

how do you make x the subject in
\(\displaystyle y=\sqrt{x \over 3}\)
 
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  • #2
Ellie said:
how do u make x the subject in
y=2x squared +3
(Wave)

$y= 2x^2+3 \Rightarrow 2x^2=y-3 \Rightarrow x^2=\frac{y-3}{2} \Rightarrow x= \pm \sqrt{\frac{y-3}{2}}$

Notice that it has to be $y-3 \geq 0 \Rightarrow y \geq 3$.
Ellie said:
how do you make x the subject in
y=\sqrt{xover3

Give it a try? (Thinking)
 
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  • #3
Hello, Ellie and welcome to MHB! :D

I have moved your thread since our "Introductions" subforum is meant for folks to post a bit about themselves to let our community know a bit about you.

I have retitled your thread so that is briefly describes the nature of the questions being asked.

We also ask that when you post questions, you show what you have tried so our helpers can see where you are stuck or what you may be doing wrong, and this way we can offer better help.

I am thinking your first equation is:

\(\displaystyle y=2x^2+3\)

What do you think is the first thing we should do in an effort to solve for $x$?
 
  • #4
evinda said:
(Wave)

$y= 2x^2+3 \Rightarrow 2x^2=y-3 \Rightarrow x^2=\frac{y-3}{2} \Rightarrow x= \pm \sqrt{\frac{y-3}{2}}$

Notice that it has to be $y-3 \geq 0 \Rightarrow y \geq 3$.
Perhaps you had already noticed this, and I would agree that it is good to point out \(\displaystyle y \geq 3\) anyway, but I should point out that this condition is satisfied by the given equation.

-Dan
 
  • #5


To make x the subject in an equation, we need to isolate it on one side of the equation by using algebraic operations. In the first equation, y=2x^2 +3, we can make x the subject by first subtracting 3 from both sides to get y-3=2x^2. Then, we can divide both sides by 2 to get (y-3)/2=x^2. Finally, we can take the square root of both sides to get x=\sqrt{(y-3)/2}.

In the second equation, y=\sqrt{x \over 3}, we can make x the subject by first squaring both sides to get y^2=x/3. Then, we can multiply both sides by 3 to get 3y^2=x. Thus, x=3y^2.
 

FAQ: Making x the subject in two equations

How do I change the subject in two equations?

To change the subject in two equations, you need to follow the steps of solving a system of equations. Start by isolating one variable in one equation and substitute its value into the other equation. Then, solve for the remaining variable. Finally, substitute the value of the second variable into the first equation to find the value of the original subject.

Can I make any variable the subject in two equations?

Yes, you can make any variable the subject in two equations as long as the two equations contain both variables. If one of the equations does not have the variable you want to make the subject, you will need to rearrange the equations to include it.

Do I always have to solve for both variables when making one the subject in two equations?

No, you do not always have to solve for both variables. If one of the equations only has one variable, you can simply substitute its value into the other equation and solve for the remaining variable.

What if I have more than two equations and want to make a specific variable the subject?

If you have more than two equations, you can still make a specific variable the subject by using the same steps as solving a system of equations. You will need to isolate the desired variable in one equation and substitute its value into the other equations until you have only one equation left with the variable you want as the subject.

Can I use this method to solve for multiple variables at once?

Yes, you can use this method to solve for multiple variables at once. If you have more than two equations, you will need to continue substituting the values of the solved variables into the remaining equations until you have solved for all the desired variables.

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