solve the following pairs of simultaneous equation: x+y=7, x^2+y^2=25

Question

anonymous · Answer

can somebody show me how to solve this? I did it, but when i checked it's wrong

diyadiya · Answer

x+y=7
therefore x = 7-y

Replace x with 7-y in the equation $x^2+y^2 = 25$
can you do that?

diyadiya · Answer

$$(x)^2+(y)^2=25$$$$(7-y)^2+(y)^2=25$$

diyadiya · Answer

@nnpatricia is this clear?

anonymous · Answer

yes! i've done that. making y=7-x. then later it leads to this 2x^2-14x-74. do you know how to factorize them?

diyadiya · Answer

I guess you did a small mistake there

$$x^2 + (7-x)^2 =25$$$$x^2 + x^2 -14x + 49  =25$$$$2x^2 -14x + 24  =0$$

diyadiya · Answer

did you understand where you went wrong?

phi · Answer

(7-x)^2   or (7-x)(7-x)
use FOIL  First
7*7= 49
OUTER   7*-x= -7x
INNER  -x*7  = -7x
LAST  -x*-x= x^2
add up the four terms to get x^2-14x+49
use this in your original equation
x^2 +(7-x)^2 = 25   (replace (7-x)^2 with the expanded form)
x^2 + x^2-14x+49= 25

simplify by subtracting 25 from both sides of the equation
add the 2 x^2 terms:
2x^2-14x+24=0

notice that all the terms are even, so simplify by dividing by 2:
x^2-7x+12= 0/2   or just
x^2-7x+12=0

anonymous · Answer

@Diyadiya yes! thanks :)

phi · Answer

the plus sign on the 3rd term  +12 means both factors have the same sign
the minus sign on the 2nd term -7x   means the factors are negative

anonymous · Answer

@phi thanks for the very clear explanation too :)

phi · Answer

to factor,  list the factors of the last term  +12:  1,12  3,4
do any add up to 7?  yes!