Question 178816
Elimination is the easiest way to solve this system.

{{{system(3x-5y=7,2x+5y=13)}}}

Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

{{{(3x-5y)+(2x+5y)=(7)+(13)}}}

{{{(3x+2x)+(-5y+5y)=7+13}}} Group like terms.

{{{5x+0y=20}}} Combine like terms.

{{{5x=20}}} Simplify.

{{{x=(20)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.

{{{x=4}}} Reduce.

------------------------------------------------------------------

{{{3x-5y=7}}} Now go back to the first equation.

{{{3(4)-5y=7}}} Plug in {{{x=4}}}.

{{{12-5y=7}}} Multiply.

{{{-5y=7-12}}} Subtract {{{12}}} from both sides.

{{{-5y=-5}}} Combine like terms on the right side.

{{{y=(-5)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.

{{{y=1}}} Reduce.

So our answer is {{{x=4}}} and {{{y=1}}}.

Which form the ordered pair *[Tex \LARGE \left(4,1\right)].

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(4,1\right)]. So this visually verifies our answer.

{{{drawing(500,500,-6,14,-9,11,
grid(1),
graph(500,500,-6,14,-9,11,(7-3x)/(-5),(13-2x)/(5)),
circle(4,1,0.05),
circle(4,1,0.08),
circle(4,1,0.10)
)}}} Graph of {{{3x-5y=7}}} (red) and {{{2x+5y=13}}} (green)
The passage provides a detailed solution to a system of linear equations using the elimination method, and it includes the final answer.
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
Question 178816
Elimination is the easiest way to solve this system.

{{{system(3x-5y=7,2x+5y=13)}}}

Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

{{{(3x-5y)+(2x+5y)=(7)+(13)}}}

{{{(3x+2x)+(-5y+5y)=7+13}}} Group like terms.

{{{5x+0y=20}}} Combine like terms.

{{{5x=20}}} Simplify.

{{{x=(20)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.

{{{x=4}}} Reduce.

------------------------------------------------------------------

{{{3x-5y=7}}} Now go back to the first equation.

{{{3(4)-5y=7}}} Plug in {{{x=4}}}.

{{{12-5y=7}}} Multiply.

{{{-5y=7-12}}} Subtract {{{12}}} from both sides.

{{{-5y=-5}}} Combine like terms on the right side.

{{{y=(-5)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.

{{{y=1}}} Reduce.

So our answer is {{{x=4}}} and {{{y=1}}}.

Which form the ordered pair *[Tex \LARGE \left(4,1\right)].

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(4,1\right)]. So this visually verifies our answer.

{{{drawing(500,500,-6,14,-9,11,
grid(1),
graph(500,500,-6,14,-9,11,(7-3x)/(-5),(13-2x)/(5)),
circle(4,1,0.05),
circle(4,1,0.08),
circle(4,1,0.10)
)}}} Graph of {{{3x-5y=7}}} (red) and {{{2x+5y=13}}} (green)
user
The passage provides a detailed solution to a system of linear equations using the elimination method, and it includes the final answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER