System of Equations and Inequalities

[Everstar]

Homework Statement

Solve each sysytem usiing any method you wish:
x²-y²=21
x+y=7

Homework Equations

x²-y²=21
x+y=7

The Attempt at a Solution

I chose to do the substitution method.

so i change equation 2 to this: y=7-x and substitute it into the other equation in place of y.

so now equation 1 is this x²-(7-x)²=21

so i foil out that part to get x²-(49-14x+x²)=21

now this is where I am stuck I am not sure what to doo because I am not sure if the - outside the paranthesis turns everything inside them to the oposite sign? or what?

 

[rock.freak667]

so i foil out that part to get x²-(49-14x+x²)=21

now this is where I am stuck I am not sure what to doo because I am not sure if the - outside the paranthesis turns everything inside them to the oposite sign? or what?

Right the -ve or '-1' in front of the bracket, multiplies everything inside by -1. So expand out.

 

[Everstar]

so i would get x²-49+14x-x²=21?

 

[rock.freak667]

so i would get x²-49+14x-x²=21?

Yes.

 

[Everstar]

so would equal -2 is what i got then i sustituted that into y=7-(-2) to get y =9.

those would be my anwser correct?

 

[rock.freak667]

so would equal -2 is what i got then i sustituted that into y=7-(-2) to get y =9.

those would be my anwser correct?

if you sub that into the first equation you do not get 21, check it over.

 

[Everstar]

yeah but it work for the 2nd equation what did i do wrong did i skip something?

 

[Everstar]

woops haha i was doing something wrong with my math i found x actally equal 5 and y= 2

 

[rock.freak667]

woops haha i was doing something wrong with my math i found x actally equal 5 and y= 2

That should be right now