How do you solve the following linear system 3x-7y=1, x+3y=1? ?

Jun 23, 2018

Multiply the second equation by $3$ (everything) and then subtract the second equation from the first

Explanation:

So if you multiply the 2nd equation by $3$, you have

$3 x + 9 y = 3$

The first one is

$3 x - 7 y = 1$

Now, after subtracting them. we have:

$16 y = 2$

so

$y = \frac{1}{8}$

Now simply put it into any equation from the initial part (let's say the second). We have

$x + 3 \cdot \frac{1}{8} = 1$

So

$x = \frac{5}{8}$

$y = \frac{1}{8}$

is the only solution.
The text contains a mathematical question about solving a linear system, and it provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
How do you solve the following linear system 3x-7y=1, x+3y=1? ?

Jun 23, 2018

Multiply the second equation by $3$ (everything) and then subtract the second equation from the first

Explanation:

So if you multiply the 2nd equation by $3$, you have

$3 x + 9 y = 3$

The first one is

$3 x - 7 y = 1$

Now, after subtracting them. we have:

$16 y = 2$

so

$y = \frac{1}{8}$

Now simply put it into any equation from the initial part (let's say the second). We have

$x + 3 \cdot \frac{1}{8} = 1$

So

$x = \frac{5}{8}$

$y = \frac{1}{8}$

is the only solution.
user
The text contains a mathematical question about solving a linear system, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER