Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
