Ask & Answer Question

The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is:

Option 1 -

$(3, \frac{1}{3})$

Option 2 -

$(- 3, \frac{1}{3})$

Option 3 -

$(- 3, - \frac{1}{3})$

Option 4 -

$(3, - \frac{1}{3})$

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 2

Detailed Solution:

System of equation can be written as

$(\begin{matrix} 3 & - 2 & 1 \\ 5 & - 8 & 9 \\ 2 & 1 & a \end{matrix}) (\begin{array}{l} x \\ y \\ z \end{array}) = (\begin{array}{l} b \\ 3 \\ - 1 \end{array})$

$(\begin{matrix} 3 & - 2 & 1 \\ 15 & - 24 & 27 \\ 6 & 3 & 3 a \end{matrix}) (\begin{array}{l} x \\ y \\ z \end{array}) = (\begin{array}{l} b \\ 9 \\ - 3 \end{array})$

$R_{3} - 2 R_{1}, R_{2} - 5 R_{1}$

for no solution

3a + 9 = 0 but $\frac{3}{2} - \frac{9 b}{2} \neq 0$

$\Rightarrow a = - 3 \Rightarrow b \neq \frac{1}{3}$

System of equation can be written as <math> <mrow> <mrow> <mo>(</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mn>3</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>2</mn> </mtd> <mtd columnalign="center"> <mn>1</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mn>5</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>8</mn> </mtd> <mtd columnalign="center"> <mn>9</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mn>2</mn> </mtd> <mtd columnalign="center"> <mn>1</mn> </mtd> <mtd columnalign="center"> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi>b</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </math> <math> <mrow> <mrow> <mo>(</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mn>3</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>2</mn> </mtd> <mtd columnalign="center"> <mn>1</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mn>1</mn> <mn>5</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>2</mn> <mn>4</mn> </mtd> <mtd columnalign="center"> <mn>2</mn> <mn>7</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mn>6</mn> </mtd> <mtd columnalign="center"> <mn>3</mn> </mtd> <mtd columnalign="center"> <mn>3</mn> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi>b</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>9</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>−</mo> <mn>2</mn> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mn>5</mn> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </math> for no solution3a + 9 = 0 but <math> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>−</mo> <mfrac> <mrow> <mn>9</mn> <mi>b</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>≠</mo> <mn>0</mn> </mrow> </math> <math> <mrow> <mo>⇒</mo> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo>⇒</mo> <mi>b</mi> <mo>≠</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
686k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

The ordered pair (a, b), for which the system of linear equations 3x – 2y + z = b 5x – 8y + 9z = 3 2x + y + az = -1 has no solution, is:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is: