What is x+y=1,x^2-2x+3y=-1 ?

The solution to x+y=1,x^2-2x+3y=-1 is

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x+y=1,x^2-2x+3y=-1

x + y = 1, x^{2} - 2 x + 3 y = - 1

(x = 1, x = 4, y = 0 y = - 3)

Solution steps

[x + y = 1 x^{2} - 2 x + 3 y = - 1]

Isolate

x

for

x + y = 1 : x = 1 - y

Plug the solutions

x = 1 - y

into

x^{2} - 2 x + 3 y = - 1

For

x^{2} - 2 x + 3 y = - 1

, subsitute

x

with

1 - y : y = 0, y = - 3

Plug the solutions

y = 0, y = - 3

into

x + y = 1

For

x + y = 1

, subsitute

y

with

0 : x = 1

For

x + y = 1

, subsitute

y

with

- 3 : x = 4

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x + y = 1, x^{2} - 2 x + 3 y = - 1

are

(x = 1, x = 4, y = 0 y = - 3)

x + 2 y = 1, 2 x^{2} + 2 y = 42

x + 2 y = 2, x + 2 y = 6

8 a = 4, b = 3 c

x^{2} + y^{2} + 4 x - 6 y - 12 = 0, x^{2} + y^{2} - 8 x + 6 y + 12 = 0

x + y = 1, y - 15 = - x^{2} + 4 x