x(k+1)+y(2+k)-3=3x+2y=2x-3y+1 what is the value of k?

Answer 1

x(k + 1) + y(2 + k) - 3 + 3x + 2y = 2x - 3y + 1

There are two = signs, so I'm going to assume the first one is meant to be a plus.

To solve for this equation, expand the left hand side.

xk + x + 2y + yk - 3 + 3x + 2y = 2x - 3y + 1

Now, group like-terms.

xk + 4x + 4y + yk - 3 = 2x - 3y + 1

Now, keep everything with a k in it on the left hand side; move everything else to the right hand side.

xk + yk = 2x - 3y + 1 - 4x - 4y + 3

Simplify the right hand side.

xk + yk = -2x - 7y + 4

Factor a k out of the left hand side

k(x + y) = -2x - 7y + 4

And now, divide both sides by (x + y)

k = (-2x - 7y + 4) / (x + 4)

Answer 2

since there is three unknowns; x, y and k but there is only two equations
x(k+1) + y(k+2) - 3 = 3x + 2y
and
3x + 2y = 2x - 3y + 1
note, x(k+1) + y(k+2) -3 = 2x -3y +1 is redundant.

here we have more unknowns then equations, so we have open ended answer, that's

k = (5 - 10y) / (1 - 4y), y is real

so, y can be any number
for example, when y =0, x=1, k=5

or when y = -1, x=6, k=3 and so on.

basically, need 3 equations to solve 3 unknowns.
when unknowns > equations, open end solution.
when equations > unknowns, fix value solution, the extra equations can be used for counter checking.

however, if the equations is not valid

for example
a + b = 3
a + b = 5

2 unknowns, 2 equations, there should be a solutions but since the equations is impossible then there is no solutions.

sorry for my bad English

Answer 3

the way your present this question I dont think its right. the equal signs can not have 2 of them but you would multiply out of the parantheses first then combine like terms. isolate the letter on one side by subtracting from the other side of the equal sign. repost if this problemn was typed wrong by you then i can help better