Answer:
Option is d) Coincident lines.
Step-by-step explanation:
Given:
x = 2 - y and
3x + 3y = 6
Solution:
Let we rewrite the equations as
x + y = 2 ...................................Equation ( 1 )
3x + 3y = 6 ....................................Equation ( 2 )
Compare the above Two Equations with the following
a₁x + b₁y = c₁ and
a₂x + b₂y = c₂
We get
a₁ = 1 ; b₁ = 1 ; c₁ = 2 and
a₂ = 3 ; b₂ = 3 ; c₂ = 6
Now we will check
[tex]\frac{a_{1}}{a_{2}}=\frac{1}{3}\\\\\frac{b_{1}}{b_{2}}=\frac{1}{3}\\\\\frac{c_{1}}{c_{2}}=\frac{2}{6}=\frac{1}{3} \\[/tex]
Now we get
[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}[/tex]
Which is the condition for a COINCIDENT LINES
COINCIDENT LINES have Infinite solutions for different x and different y
