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One equation of a pair of dependent linear equations is \( -5 x+7 y=2 \). To do: We have to find the second equation. Solution: We know that, The condition for dependent linear equations is, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{k}$ \( -5x+7y-2=0 \) Here, $a_1=-5, b_1=7, c_1=-2$ For $k=2$, $a_2=2(-5)=-10, b_2=2(7)=14, c_2=2(-2)=-4$ Therefore, The required dependent linear equation is $a_2x+b_2y+c_2=0$, i.e., $-10x+14y-4=0$ $\Rightarrow 10x-14y+4=0$ Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Solution Answer - D Condition for dependent linear equations a1a2=b1b2=c1c2=1k Given equation of line is – 5x + 7y – 2 = 0 Here, a1=−5,b1=7, c1=−2 From Eq.(i)−5a2=7b2=−2c2=1k⇒ a2=−5k, b2=7k, c2=−2k Where, k is any arbitrary constant Putting k = 2, then a2=−10,b2=14 And c2=−4 ∴ The required equation of line becomes a2x+b2y+c2=0 ⇒ -10x + 14y – 4 = 0 ⇒ 10x – 14y + 4 = 0 Or, 10x – 14y = -4Solve Textbooks Question Papers What is a pair of dependent linear equation?Given, one equation of a pair of dependent linear equations is -5x + 7y = 2. We have to find the second equation. A pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is is dependent and consistent,if a1a2=b1b2=c1c2. Here, a₁ = -5, b₁ = 7, c₁ = -2.
Can 2 linear equations have 2 solutions?Number of Solutions
Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.) The word unique in this context means there is a solution, and it's the only one.
What is dependent linear equation example?The two equations y=2x+5 and y=4x+3 , form a system of equations . The ordered pair that is the solution of both equations is the solution of the system. A system of two linear equations can have one solution, an infinite number of solutions, or no solution.
When a system of linear equations in two variables is dependent?The two lines have different slopes and intersect at one point in the plane. A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line.
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