SOLUTION: please solve this algebra: 2-x+y=3-y+x

Question 949663: please solve this algebra: 2-x+y=3-y+x
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

....you have a linear equation and graph is a line
x-intercept:

so, x-intercept is at (,)
y-intercept:

so, x-intercept is at (,)
plot points and draw a line through:

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

start with 2-x+y = 3-y+x

add y to both sides of the equation to get:

2-x+2y = 3+x

add x to both sides of the equation to get:

2+2y = 3+2x

subtract 2 from both sides of the equation to get:

2y = 1+2x

divide both sides of the equation by 2 to get:

y = 1/2 + x

rearrange the terms to get:

y = x + 1/2

your original equation of 2 - x + y = 3 - y + x is true when y = x + 1/2.

for example:

let x = 2 and y = 2.5

2 - x + y becomes 2 - 2 + 2.5 which becomes 2.5.

3 - 2.5 + 2 becomes 5 - 2.5 which becomes 2.5.

your original equation of 2-x+y = 3-y+x is true when y = x + 1/2.

just to confirm some more, use another value of x and y that satisfy the equation of y = x + 1/2.

let x = 15 and y = 15.5

2 - x + y becomes 2 - 15 + 15.5 which becomes -13 + 15.5 which becomes 2.5.

3 - y + x becomes 3 - 15.5 + 15 which becomes 18 - 15.5 which becomes 2.5.

it doesn't matter what the value of x and y are as long as y = x + 1/2.

when y = x + 1/2, the value of the expression on the left side of the equation and on the right side of the equation will always be equal to 2.5.

the answer to your question is that the original equation will always be true when y = x + 1/2.

the reason why each side of the equation will always be equal to 2.5 is shown below:

start with 2 - x + y = 3 - y + x

let y = x + 1/2.

the equation becomes:

2 - x + (x + 1/2) = 3 - (x + 1/2) + x

simplify to get:

2 - x + x + 1/2 = 3 - x - 1/2 + x

combine like terms to get:

2 + 1/2 = 3 - 1/2

combine like terms again to get:

2 and 1/2 = 2 and 1/2 which is the same as 2.5 = 2.5

when you asked to solve this, i presume you asked to solve for y in terms of x.

that answer is that y = x + 1/2.

as long as y = x + 1/2, the original equation will be true.

the fact that each side of the equation will always be equal to 2.5 when you replace y with x + 1/2 is additional information that i don't believe you needed to know, although you might find it interesting.

at least i did.
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