Question

Solve the system : x = 2 - y and 3x + 3y = 6

Answer 1

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

$\frac{a_{1}}{a_{2}}=\frac{1}{3}\\\\\frac{b_{1}}{b_{2}}=\frac{1}{3}\\\\\frac{c_{1}}{c_{2}}=\frac{2}{6}=\frac{1}{3}$

Now we get

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}$

Which is the condition for a  COINCIDENT LINES

COINCIDENT LINES have Infinite solutions for different x and different y