Question

find the combined equations of lines x+y-2=0 and 2x-y+=0​

Answer 1

Ans:-

when we combined

x+y-2+2x-y +2=0

+y and -y +2 and -2 will be cancelled

3/=0 will be answer

Answer 2

Given :

• x+y-2=0 ....Equation(1)

• 2x-y+2=0 ....Equation(2)

To Find :

•The combined equation of both lines =?

Solution :

➡ The combined equation will be,

$\red\bigstar\boxed{\sf{(ax_{1}+by_{1}+cy_{1})(ax_{2}+by_{2}+cy_{2})=0}}$

• Multiplying both equations (1) and (2).

$\\ \implies \sf \: (x + y - 2)(2x - y + 2) = 0$

$\\ \implies \sf \: x(2x - y + 2) + y(2x - y + 2) - 2(2x - y + 2) = 0\\ \\ \\ \implies \sf 2 {x}^{2} - xy + 2x + 2xy - {y}^{2} + 2y - 4x + 2y - 4 = 0 \\ \\ \\ \implies \sf \: 2 {x}^{2} + xy - 2x - {y}^{2} + 4y - 4 = 0 \\ \\ \\ \implies \sf \: 2 {x}^{2} - {y}^{2} - 2x + 4y + xy - 4 = 0$

The combined equation is :

$\red \bigstar \boxed{ \sf{2 {x}^{2} - {y}^{2} - 2x + 4y + xy - 4 = 0}}$