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Testing linear equation with two variables.

Bing solved easily. ChatGPT gone wild.

Find the solution for this equation where both x and y are integers and greater than zero:

First, we can rewrite the equation as:

This gives us x = 5/2, which is not an integer greater than zero.

This gives us x = -1/2, which is not an integer greater than zero.

This gives us x = -7/2, which is not an integer greater than zero.

This gives us x = -13/2, which is not an integer greater than zero.

If we fix x = 1, then we can solve for y as follows:

Not being able to set temperature opens it up to that. I wonder what bing is doing differently?

This method doesn't seem to work.

I personally favor Wolfram Alpha and recommend I’d highly. I’ll use this as a test case. Thanks

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## How to Solve Math Problems Faster: 15 Techniques to Show Students

Here are 15 techniques to show students, helping them solve math problems faster:

## Addition and Subtraction

The first step is to add what’s easy. The second step is to add the rest.

With this fast technique, big numbers won’t look as scary now.

## 2. Two-Step Subtraction

There’s a similar method for subtraction.

Remove what’s easy. Then remove what’s left.

Instead of two complex numbers, students will only have to tackle one.

## 3. Subtracting from 1,000

You can give students confidence to handle four-digit integers with this fast technique.

Let’s say students must solve 1,000 – 438. Here are the steps:

This also applies to 10,000, 100,000 and other integers that follow this pattern.

## Multiplication and Division

Using 33 x 48 as an example, here’s the process:

The only prerequisite is understanding the 2 times table.

## 5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

Here’s what to do: For each power of 2 that makes up that number, double the other number.

## 6. Multiplying by 9

But there’s an easy tactic to solve this issue, and it has two parts.

Despite more steps, altering the equation this way is usually faster.

There’s an easier way for multiplying two-digit integers by 11.

Let’s say students must find the product of 11 x 34.

It’s multiplication without having to multiply.

## 8. Multiplying Even Numbers by 5

This technique only requires basic division skills.

The result is 30, which is the correct answer.

It’s an ideal, easy technique for students mastering the 5 times table.

## 9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps, which 5 x 7 exemplifies.

## 10. Squaring a Two-Digit Number that Ends with 1

Squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

There are four steps to this shortcut, which 812 exemplifies:

- Subtract 1 from the integer: 81 – 1 = 80
- Square the integer, which is now an easier number: 80 x 80 = 6,400
- Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560
- Add 1: 6,560 + 1 = 6,561

## 11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are only two parts of the process.

First, students will always make 25 the product’s last digits.

Just like that, a hard problem becomes easy multiplication for many students.

## 12. Calculating Percentages

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

## 13. Balancing Averages

With practice, this method may not even require pencil and paper. That’s how easy it is.

## Word Problems

This isn’t a trick. It’s a tactic.

Teach students to look for these buzzwords, and what skill they align with in most contexts:

As a result, they should have an easier time processing word problems .

## 15. Creating Sub-Questions

Each student should ask him or herself:

- What am I looking for? — Students should read the question over and over, looking for buzzwords and identifying important details.
- What information do I need? — Students should determine which facts, figures and variables they need to solve the question. For example, if they determine the question is rooted in subtraction, they need the minuend and subtrahend.
- What information do I have? — Students should be able to create the core equation using the information in the word problem, after determining which details are important.

These sub-questions help students avoid overload.

## Final Thoughts About these Ways to Solve Math Problems Faster

Showing these 15 techniques to students can give them the confidence to tackle tough questions .

A rewarding class equals an engaging class . That’s an easy equation to remember.

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## Eagle sixth grader will compete in national math competition

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## How to Solve Math Problems

Last Updated: May 23, 2022 References Approved

## Understanding the Problem

- Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems. [7] X Research source
- Draw a graph or chart. [8] X Research source
- Arrange the components of the problem on a line. [9] X Research source
- Draw simple shapes to represent more complex features of the problem. [10] X Research source

## Developing a Plan

## Solving the Problem

## Expert Q&A Did you know you can get expert answers for this article? Unlock expert answers by supporting wikiHow

Support wikiHow by unlocking this expert answer.

- Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. ⧼thumbs_response⧽ Helpful 1 Not Helpful 0
- Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

## You Might Also Like

- ↑ http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.pdf
- ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
- ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
- ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
- ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

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