# How do you solve the following system?:  3x-2y=4 , x-4y=3

Nov 19, 2015

I found:
$x = 1$
$y = - \frac{1}{2}$

#### Explanation:

We can isolate $x$ from the second equation and substitute into the first to find $y$:
$x = 4 y + 3$
Into the first:
$3 \left(\textcolor{red}{4 y + 3}\right) - 2 y = 4$
$12 y + 9 - 2 y = 4$
$10 y = - 5$
$y = - \frac{5}{10} = - \frac{1}{2}$
Use this value back into:
$x = 4 \left(\textcolor{red}{- \frac{1}{2}}\right) + 3 = - 2 + 3 = 1$
The text contains a mathematical question about solving a system of linear equations, and it provides a detailed solution with the final answers for x and y.
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 system?:  3x-2y=4 , x-4y=3

Nov 19, 2015

I found:
$x = 1$
$y = - \frac{1}{2}$

#### Explanation:

We can isolate $x$ from the second equation and substitute into the first to find $y$:
$x = 4 y + 3$
Into the first:
$3 \left(\textcolor{red}{4 y + 3}\right) - 2 y = 4$
$12 y + 9 - 2 y = 4$
$10 y = - 5$
$y = - \frac{5}{10} = - \frac{1}{2}$
Use this value back into:
$x = 4 \left(\textcolor{red}{- \frac{1}{2}}\right) + 3 = - 2 + 3 = 1$
user
The text contains a mathematical question about solving a system of linear equations, and it provides a detailed solution with the final answers for x and y.

TYPE: SINGLE_QUESTION_WITH_ANSWER