Solve the following simultaneouse equation. 3x+y=1 and x²+y²=5

x=2/5, y=11/5

or x=-1y = 2

Step-by-step explanation:

Substitute y=3x+1 in x2+y2=5 to obtain

x2 + (3x+1) 2=5 ⇒ 10x2+6x-4=0

Hence

5x2+3x-2=0 ⇒ 5x2+5x-2x-2=0 ⇒5x (x+1) - 2 (x+1) = 0 ⇒ (5x-2) (x+1) = 0

Hence

either

x=2/5, y=3*2/5+1=11/5

or x=-1, y=3 * (-1) + 1 = - 2