3 years ago

How do you solve this?

Mathematics

1 answer:

Paul [167]3 years ago

4 0

You need to use percentage I would help but I can’t because of I’m bad at percentages

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For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

viktelen [127]

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

$3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)$

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

$x_{2}=3x_{1} -2$

substitute in equation (2), we get

$9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k$

we cannot find the value of $x_{1}$ and $x_{2}$ .

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

$3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6$

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

4 0

3 years ago

How do you solve this?​

How do you solve this?