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# x-y=x+y+17

0
873
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x-y=x+y+17

x= ?

y= ?

Mar 25, 2015

#1
+2353
+5

First we solve the equation for y

$$\begin{array}{lcl} x - y = x + y + 17\\ -y = y + 17\\ -2y = 17\\ y = -\frac{17}{2} \end{array}$$

We have 2 possible situations for x

either

$$\begin{array}{lcl} y = -\frac{17}{2}\\ \end{array}$$

and we find

$$\begin{array}{lcl} x - y = x + y + 17\\ x + \frac{17}{2} = x - \frac{17}{2} + 17\\ x = x - 17 + 17\\ x = x \end{array}$$

Which means x can be any number,

or

$$\begin{array}{lcl} y \neq -\frac{17}{2}\\ \end{array}$$

and we find no value for x for which the equation holds.

Reinout

Mar 25, 2015

#1
+2353
+5

First we solve the equation for y

$$\begin{array}{lcl} x - y = x + y + 17\\ -y = y + 17\\ -2y = 17\\ y = -\frac{17}{2} \end{array}$$

We have 2 possible situations for x

either

$$\begin{array}{lcl} y = -\frac{17}{2}\\ \end{array}$$

and we find

$$\begin{array}{lcl} x - y = x + y + 17\\ x + \frac{17}{2} = x - \frac{17}{2} + 17\\ x = x - 17 + 17\\ x = x \end{array}$$

Which means x can be any number,

or

$$\begin{array}{lcl} y \neq -\frac{17}{2}\\ \end{array}$$

and we find no value for x for which the equation holds.

Reinout

reinout-g Mar 25, 2015