Mathematics
OpenStudy (anonymous):

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

OpenStudy (texaschic101):

add the equations and what do you get ?

OpenStudy (anonymous):

no solution?

OpenStudy (anonymous):

@texaschic101

OpenStudy (anonymous):

OpenStudy (texaschic101):

what did you get when you added them ?

OpenStudy (texaschic101):

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.

OpenStudy (texaschic101):

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

OpenStudy (anonymous):

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 }$