# How do you solve 4x+y=13 and 2x-y=5?

Aug 1, 2015

Add the 2 equations together to get a third equation with the $y$ term eliminated; solve for $x$; replace $x$ in one of the given equations with the solution to find $y$
$\left(x , y\right) = \left(3 , 1\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$4 x + y = 13$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$2 x - y = 5$

[3]$\textcolor{w h i t e}{\text{XXXX}}$$6 x = 18$

Divide both sides by $6$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = 3$

Substitute $3$ for $x$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$4 \left(3\right) + y = 13$

Simplify
[6]$\textcolor{w h i t e}{\text{XXXX}}$$12 + y = 13$

Subtract $12$ from both sides
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 1$
The text passage contains a mathematical question involving solving a system of linear equations, 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 4x+y=13 and 2x-y=5?

Aug 1, 2015

Add the 2 equations together to get a third equation with the $y$ term eliminated; solve for $x$; replace $x$ in one of the given equations with the solution to find $y$
$\left(x , y\right) = \left(3 , 1\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$4 x + y = 13$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$2 x - y = 5$

[3]$\textcolor{w h i t e}{\text{XXXX}}$$6 x = 18$

Divide both sides by $6$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = 3$

Substitute $3$ for $x$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$4 \left(3\right) + y = 13$

Simplify
[6]$\textcolor{w h i t e}{\text{XXXX}}$$12 + y = 13$

Subtract $12$ from both sides
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 1$
user
The text passage contains a mathematical question involving solving a system of linear equations, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER