show the lines having the equations 3x + 5y + 7 = 0 and 6x + 10y - 5 = 0 are parallel. Sketch the graph
Answers
EXPLANATION.
Equations :
⇒ 3x + 5y + 7 = 0. - - - - - (1).
⇒ 6x + 10y - 5 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 3x + 5y + 7 = 0. - - - - - (1).
Taking y axis it means x = 0.
Put the value of x = 0 in the equation, we get.
⇒ 3(0) + 5y + 7 = 0.
⇒ 5y + 7 = 0.
⇒ 5y = - 7.
⇒ y = - 7/5.
⇒ y = - 1.4.
Their Co-ordinates = (0,-1.4).
Taking x axis it means y = 0.
Put the value of y = 0 in the equation, we get.
⇒ 3x + 5(0) + 7 = 0.
⇒ 3x + 7 = 0.
⇒ 3x = - 7.
⇒ x = - 7/3.
⇒ x = - 2.33.
Their Co-ordinates = (-2.33,0).
From equation (2), we get.
⇒ 6x + 10y - 5 = 0. - - - - - (2).
Taking y axis it means x = 0.
Put the value of x = 0 in the equation, we get.
⇒ 6(0) + 10y - 5 = 0.
⇒ 10y - 5 = 0.
⇒ 10y = 5.
⇒ y = 1/2.
⇒ y = 0.5.
Their Co-ordinates = (0,0.5).
Taking x axis it means y = 0.
Put the value of y = 0 in the equation, we get.
⇒ 6x + 10(0) - 5 = 0.
⇒ 6x - 5 = 0.
⇒ 6x = 5.
⇒ x = 5/6.
⇒ x = 0.833
Their Co-ordinates = (0.833,0).
Both lines are parallel to each other and never intersects each other.
Also, we know that.
Conditions for parallel lines equation.
a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
Using this formula in the equation, we get.
Equations :
⇒ 3x + 5y + 7 = 0. - - - - - (1).
⇒ 6x + 10y - 5 = 0. - - - - - (2).
⇒ a₁ = 3, b₁ = 5 and c₁ = 7.
⇒ a₂ = 6, b₂ = 10 and c₂ = - 5.
Put the values in the equation, we get.
⇒ 3/6 = 5/10 ≠ 7/-5.
⇒ 1/2 = 1/2 ≠ - 7/5.
Hence, this lines are parallel lines.
