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### Course: College Algebra>Unit 1

Lesson 2: Solutions to linear equations

# Solutions to 2-variable equations

The solution of an equation with one variable is a number. How does the solution of a 2-variable equation look like? Well, it is an ordered pair. Learn more about it and how to test solutions to 2-variable equations.

## Want to join the conversation?

• serious question . Does anyone actually use this ? if so for what ? cus honestly i dont see the point
• Yahy,

Solving linear equations is a foundation step for solving systems of linear equations, which is a foundation step for linear programming (which, surprisingly, is not computer programming) or linear optimization.

Linear programming is a method for calculating an optimal result given a set of constraints. Linear programming is used in business all the time.

For example, if you owned a shop, you might want to know the best combination of items to stock in the limited capacity of the shop in order to maximize cash flow. Your most profitable item might not be the best selling or your space might only hold 10 of your most profitable item or 40 of a less profitable item. Linear programming helps you to determine whether to stock 5 of the most profitable item and 20 of the less profitable item or 4 of the most profitable and 30 of the less profitable to keep the cash flowing steadily.

If you don't own the shop, but you work there, you want your boss to be able to do linear programming so there is money for you to be paid.

If you are able to do the linear programming, you would be able to see whether the boss has the right idea and, perhaps, you could make a suggestion that will get you a raise.
• this video helps but I could use more help
• Linear equations are a foundation of learning linear systems. If you can review some previous work you should recognize the relationship between x and y coordinates to grind then on a 2 dimensional coordinate plane. If you need help understanding draw yourself a table labeling x and y axis
• I need some examples of linear equations in 2 variables
• how is this used in real life
• If you don't think you're going to use it, don't learn it. No one is going to force you to learn something you don't deem necessary. It's your choice.

However, when you get to a point in life when you want to help someone understand this, or you need to use it and don't have the knowledge you might feel kinda bad.

Instead of thinking of how you're not going to use it, and in what ways it inconveniences you NOW. What about the ways you'll use it? If you feel the knowledge you attain is useless, maybe become a tutor, teach others. Maybe they think it's worth more than you do.

You don't always use all knowledge in the moment, that's kind of why you learn it. You won't use it now, but you'll use it one day.

Then again, I'm not going to force you to learn anything.Your choice.
• I feel like this is pretty simple math but what is it used for in real life?
• Linear equations are used in real life for modeling relationships between variables in fields such as economics, business, engineering, physics, finance, computer science, environmental science, transportation, social sciences, medicine, and sports analytics. They help optimize systems, analyze data, and solve problems across various domains.
• WHY is this so confusing? Sinks into Confusion
• serious question . Does anyone actually use this ? if so for what ? cus honestly i dont see the poin
• Sometimes no you won't use a few things you learn in school for in real life. But the whole point of this is so when you do need it, you will notice that you learned it in school!

And even if you can't think of a reason, you will still need to know this to continue in school and learn things that you will need to know for the real world.

And if that can't even be used in real life, then just have fun learning!
• How can I solve an equation with two variables? An equation like ' 2x + 4y =100 solve for y and x '
• Solving for a variable is also called isolating the variable, so you want to move everything away from it.
To isolate y, first subtract 2x from both sides (4y = -2x + 100), then divide by 4 (y = -1/2 x + 25). This is the more common usage because this is a linear function in slope intercept form - y in terms of x or y dependent on x.
To solve for x, subtract 4y from both sides (2x = - 4y + 100), then divide by 2 (x = - 2y + 50).
• I have a question
9b-5=2
what is b?
• For the equation, what you do to one side you do to the other. And you want b to "be" alone in order to find out what number it equals!

As such:
9b - 5 = 2 get rid of the 5 by adding 5
+5 +5 remember to add to both sides!

Then you have 9b = 7
9b is actually 9 x b, and in order to remove multiplication you need to divide. So divide both sides by 9.

9b = 7 7 divided by 9 (7/9) is 0.777777... So for simplicity I would leave it as a fraction, unless stated otherwise.

Therefor, you get b = 7/9

For a more literal answer, the b in 9b - 5 = 2 is a letter, otherwise known as a variable.

Hope this helps!