left(4-x-yright)^2=x^2+y^2 eching

$${ \left(4-x-y \right) }^{ 2 } = { x }^{ 2 } + { y }^{ 2 }$$

x uchun yechish

$$x=-\frac{4\left(2-y\right)}{y-4}$$

$$y\neq 4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

4-x-y kvadratini chiqarish.

$$x^{2}+2xy-8x+y^{2}-8y+16=x^{2}+y^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+2xy-8x+y^{2}-8y+16-x^{2}=y^{2}$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$2xy-8x+y^{2}-8y+16=y^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$2xy-8x-8y+16=y^{2}-y^{2}$$

0 ni olish uchun y^{2} va -y^{2} ni birlashtirish.

$$2xy-8x-8y+16=0$$

8y ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2xy-8x+16=8y$$

Ikkala tarafdan 16 ni ayirish.

$$2xy-8x=8y-16$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2y-8\right)x=8y-16$$

Ikki tarafini 2y-8 ga bo‘ling.

$$\frac{\left(2y-8\right)x}{2y-8}=\frac{8y-16}{2y-8}$$

2y-8 ga bo'lish 2y-8 ga ko'paytirishni bekor qiladi.

$$x=\frac{8y-16}{2y-8}$$

-16+8y ni 2y-8 ga bo'lish.

$$x=\frac{4\left(y-2\right)}{y-4}$$

y uchun yechish

$$y=-\frac{4\left(2-x\right)}{x-4}$$

$$x\neq 4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

4-x-y kvadratini chiqarish.

$$x^{2}+2xy-8x+y^{2}-8y+16=x^{2}+y^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$x^{2}+2xy-8x+y^{2}-8y+16-y^{2}=x^{2}$$

0 ni olish uchun y^{2} va -y^{2} ni birlashtirish.

$$x^{2}+2xy-8x-8y+16=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$2xy-8x-8y+16=x^{2}-x^{2}$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$2xy-8x-8y+16=0$$

8x ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2xy-8y+16=8x$$

Ikkala tarafdan 16 ni ayirish.

$$2xy-8y=8x-16$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x-8\right)y=8x-16$$

Ikki tarafini 2x-8 ga bo‘ling.

$$\frac{\left(2x-8\right)y}{2x-8}=\frac{8x-16}{2x-8}$$

2x-8 ga bo'lish 2x-8 ga ko'paytirishni bekor qiladi.

$$y=\frac{8x-16}{2x-8}$$

-16+8x ni 2x-8 ga bo'lish.

$$y=\frac{4\left(x-2\right)}{x-4}$$