Explained: "Find value(s) of k so that the linear..."

Tiffany Maldonado

Answered question

2022-04-08

Find value(s) of k so that the linear system is consistent? (Enter your answers as a comma-separated list.)

6 x_{1} - 7 x_{2} = 4

9 x_{1} + k x_{2} = - 1

Coupewopmergorlpt

Beginner2022-04-09Added 13 answers

Step 1
Given,
The lianer systems equations are

6 x_{1} - 7 x_{2} = 4

9 x_{1} + k x_{2} = - 1

We know that,
For the linear systems equations

a_{1} x + b_{1} y + = 0

to be in consistent,then the condition is

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

Step 2
Now,
The linear systems equtions are

6 x_{1} - 7 x_{2} = 4

9 x_{1} + k x_{2} = - 1

For the equotin to be consistent,we have

∴ \frac{6}{9} = \frac{- 7}{k} = \frac{4}{- 1}

So,

\Rightarrow \frac{6}{9} = \frac{- 7}{k}

\Rightarrow \frac{2}{3} = \frac{- 7}{k}

\Rightarrow 2 k = - 21

k = - \frac{21}{2}

Also,

\Rightarrow \frac{- 7}{k} = \frac{4}{- 1}

\Rightarrow 4 k = 7

\Rightarrow k = \frac{7}{4}

∴

The values of k are

- \frac{21}{2}

- \frac{7}{4}

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