Solve the system : x = 2 - y and 3x + 3y = 6a) ( 4, -2 )b) ( 1, 1 )c) Parallel linesd) Coincident lines
Accepted Solution
A:
Answer:Option is d) Coincident lines.Step-by-step explanation:Given:x = 2 - y and 3x + 3y = 6Solution:Let we rewrite the equations asx + y = 2 ...................................Equation ( 1 )3x + 3y = 6 ....................................Equation ( 2 )Compare the above Two Equations with the followinga₁x + b₁y = c₁ anda₂x + b₂y = c₂We geta₁ = 1 ; b₁ = 1 ; c₁ = 2 anda₂ = 3 ; b₂ = 3 ; c₂ = 6Now 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