Question

What is the solution of the following system?
x-y=11 and -x+y=-11

Answer 1

add the equations and what do you get ?

Answer 2

no solution?

Answer 3

@texaschic101

Answer 4

@mrivera3113 :May i help you ?:)

Answer 5

what did you get when you added them ?

Answer 6

Here is a little hint....if you answer comes out like 0 = 12, or 3 = 7, incorrect answers, then there is no solution. But if your answers comes out 0 = 0 or 5 = 5, equal answers, then there is infinite solutions.

Answer 7

so what do you think the answer to this problem is ?

Answer 8

From the first equation you can make it a function of x,\[x-y=11\]\[x=11+y\]
You can then replace the function of x into the second equation,\[-x+y=-11\]\[-(11+y)+y=-11\]\[11y+y^2=11\]\[y^2+11y-11=0\]
Apply the discriminant to this equation to see if it has answers:\[\sqrt{b^2-4ac}\]\[\sqrt{11^2-4(1)(-11)}=\sqrt{121+44}=\sqrt{165}\]
Since it does have two answers, apply the quadratic formula:\[\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]\[\frac{ -(11) \pm \sqrt{165} }{ 2(1) }=\frac{ -11 \pm \sqrt{165} }{ 2 }\]\[y=\frac{ -11 \pm \sqrt{165} }{ 2 }\]
Now use this result to calculate x, plugging in to the function of x,
\[x = 11 + y\]\[x= 11+\frac{ -11 \pm \sqrt{165} }{ 2 }=11(\frac{ 1-1 \pm \sqrt{165} }{ 2 })\]\[x=11\frac{ \pm \sqrt {165} }{ 2 }\]