Determine the value of p for which the system px + 3y = p-3 12x py p is inconsistent
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... $\esone{p x + 3 y = (p - 3)} $ \left\{\begin{matrix}p=-\frac{3\left(y+1\right)}{x-1}\text{, }&x\neq 1\\p\in \mathrm{R}\text{, }&y=-1\text{ and }x=1\end{matrix}\right. \left\{\begin{matrix}x=-\frac{3y-p+3}{p}\text{, }&p\neq 0\\x\in \mathrm{R}\text{, }&p=0\text{ and }y=-1\end{matrix}\right. Similar Problems from Web SearchSharepx+3y-p=-3 Subtract p from both sides. px-p=-3-3y Subtract 3y from both sides. \left(x-1\right)p=-3-3y Combine all terms containing p. \left(x-1\right)p=-3y-3 The equation is in standard form. \frac{\left(x-1\right)p}{x-1}=\frac{-3y-3}{x-1} Divide both sides by x-1. p=\frac{-3y-3}{x-1} Dividing by x-1 undoes the multiplication by x-1. p=-\frac{3\left(y+1\right)}{x-1} Divide -3-3y by x-1. px=p-3-3y Subtract 3y from both sides. px=-3y+p-3 The equation is in standard form. \frac{px}{p}=\frac{-3y+p-3}{p} Divide both sides by p. x=\frac{-3y+p-3}{p} Dividing by p undoes the multiplication by p. ExamplesQuestion 12 - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 BoardsLast updated at Sept. 24, 2021 by Question 12 For what value of p will the following pair of linear equations have infinitely many solutions (p – 3)x + 3y = p px + py = 12
This video is only available for Teachoo black users TranscriptQuestion 12 For what value of p will the following pair of linear equations have infinitely many solutions (p – 3)x + 3y = p px + py = 12 Given equations (p – 3)x + 3y = p px + py = 12 (p – 3)x + 3y = p (p – 3)x + 3y – p = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = (p – 3) , b1 = 3 , c1 = –p px + py = 12 px + py – 12 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = p , b2 = p , c2 = –12 Given that Equation has infinite number of solutions ∴ 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 Putting in values ((𝑝 − 3))/𝑝 = 3/𝑝 = (−𝑝)/(−12) ((𝑝 − 3))/𝑝 = 3/𝑝 = 𝑝/12 1/2 marks Solving ((𝒑 − 𝟑))/𝒑 = 𝟑/𝒑 p(p – 3) = 3p p2 – 3p = 3p p2 – 3p – 3p = 0 p2 – 6p = 0 p(p – 6) = 0 So, p = 0, 6 1/2 marks Solving 𝟑/𝒑 = 𝒑/𝟏𝟐 3 × 12 = p2 36 = p2 p2 = 36 p = ± √36 p = ± 6 So, p = 6, –6 1/2 marks Since p = 6 satisfies both equations. Hence, p = 6 is the answer 1/2 marks |
