Simultaneous equation: y=1-x, y²-xy=0?

Answer 1

Here's an out of the box solution that involves neither substitution nor elimination
x + y = 1
y*(y - x) = 0

Either y = 0 and x = 1
Or y-x = 0 ie y = x = 1/2

Solns: (1,0), (1/2, 1/2)

Answer 2

just substitue y = 1 -x into the 2nd equation.

(1-x)(1-x) - x(1-x) =0

Then solve the equation, watch out for the sign.

you ends up with

1-3x+2 x^2 = 0

(1-2x)(1-x) = 0

x = 1/2 or 1.
Then, you plug in the value of x to get the value of y

Answer 3

Ans.
y ^2-xy=o

y^2=xy y=x but given y=1-x

so it is wrong.

Answer 4

(1 - x)² - x(1 - x) = 0
1 - 2x + x² - x + x² = 0
2x² - 3x + 1 = 0
(2x - 1)(x - 1) = 0
x = 1/2 , x = 1
y = 1/2 , y = 0

(1/2,1/2) , (1,0)