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-y = x-1 how do i solve this equation

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3 Answers

If solving for y then: Divide both sides of the equation by -1, this gives: y=-x+1 or y=1-x 

if solving for x: add 1 to both sides to get x=1-y

-y = x-1 is a fairly simple equation at least with real integers.

I hope to help you understand the process of solving it so you can apply the thinking to increasingly difficult equations. If this equation is difficult for you, I will try to explain it simply.

let's try a simple trick. If you want to solve for y, then it's helpful to remove the negative from it.

that means you need to do the same thing to the x side, but since x is already positive it needs to change to -x to balance things out.

the equation now reads y = -x+1 because we have reversed the negative and positive values on both sides of the equation.

I hope this helps simplify the thinking behind solving an equation of this nature. The two previous answers above this one are both correct, but may be just a tad more complex than you need at this moment.

 

When x and y both have powers of 1 like here, you know you are dealing with the y=mx+b form. 

-y = x - 1 can also be written as -y1 = x1 - 1  with their powers.

You want to get -y = x - 1 looking like y = mx + b

Now you note that the only thing different about -y = x -1 and y = mx + b is that y is negative in your problem, you need to make it positive. 

How? 

The coefficient (number multiplying y) is -1. Multiply this coefficient with its reciprocal which is 1/-1

-1y = x - 1

-1y(1/-1) = (x - 1) (1/-1)    ------------->Note that 1/-1 is simply -1

-1y(-1) = (x -1) (-1)

y = (x(-1) - 1(-1))             ------------> distribute the -1

y = -x + 1

There is your answer. 

Comments

This is a student having difficulty with a basic equation. While the solution is perfect, i seriously doubt the student can follow the thinking easily. IMHO. I am no math whiz, and you are. Try to make it in simpler english? This I hope is constructive criticism from one who had a terrible set of math teachers in Texas in a 4000+ student 3 yr HS.

Thank you Gary for your comment; I always try to explain to my students at their own level, in a way that is easiest for them to understand. Can you tell me exactly where I need to improve in my answer to make it more simple/easier for the OP to understand. Is it a specific word, sentence, or equation that is confusing? I would appreciate your feedback. Thanks :)