Given, the pair of equations are

4x + 3y - 1 = 5 which can be written as 4x + 3y = 6

12x + 9y = 15

We have to determine if the equations represent a pair of coincident lines.

We know that,

A pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is dependent and consistent, if \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\) and the graph will be a pair of coincident lines.

Here, a₁ = 4, b₁ = 3, c₁ = -6

a₂ = 12, b₂ = 9, c₂ = -15

So, a₁/a₂ = 4/12 = 1/3

b₁/b₂ = 3/9 = 1/3

c₁/c₂ = -6/-15 = 2/5

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, the given equations do not represent a pair of coincident lines.

✦ Try This: Do the equations 4x + y - 1 = 0 and 2x + 9y = 5 represent a pair of coincident lines? Justify your answer

Given, the pair of equations are , 4x + y - 1 = 0, 2x + 9y = 5

We have to determine if the equations represent a pair of coincident lines.

Here, a₁ = 4, b₁ = 1, c₁ = -1

a₂ = 2, b₂ = 9, c₂ = -5

So, a₁/a₂ = 4/2 = 2

b₁/b₂ = 1/9

c₁/c₂ = -1/-5 = 1/5

\(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, the given equations do not represent a pair of coincident lines

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