Solve by substitution method. x+y =4 x^2 +y^2 -4x=0

inhiba5f

inhiba5f

Answered question

2022-09-05

Solve by substitution method.
x+y=4
x 2 + y 2 4 x = 0

Answer & Explanation

Bordenauaa

Bordenauaa

Beginner2022-09-06Added 18 answers

x+y =4 ........................(1)
x 2 + y 2 4 x = 0...........(2)
from(1), x =4-y
putting value of x in(2) , we get,
( 4 y ) 2 + y 2 4 ( 4 y ) = 0
=> 16 8 y + y 2 + y 2 16 + 4 y = 0
=> y 2 + y 2 8 y + 4 y + 16 16 = 0
=> 2 y 2 4 y = 0
=> 2 y ( y 2 ) = 0
hence either 2y = 0 , => y = 0 ; so x = 4 - y = 4 -0 = 4
or
y- 2 =0, => y =2; so,x = 4 - y = 4 - 2 = 2
Answer:- x = 4 ; y =0;
x = 2 ; y = 2;
themediamafia73

themediamafia73

Beginner2022-09-07Added 3 answers

Solve for y so y=4-x. Plug that into the second equation.
x 2 + ( 4 x ) 2 4 x = 0 Simplify
x 2 + 16 4 x 4 x + x 2 4 x = 0 Simplify again
2 x 2 12 x + 16 = 0 Divide by 2
x 2 6 x + 8 = 0 Now factor this and solve for x.
You get two answers so you need to plug both x values into the functions to get your corresponding y values.

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