# Linear Problem Solving Well, I like trains, but I still feel a little nervous when I read a math problem that starts with a train. Our variable here is the amount of interest, so let's call that x. Your cell phone company is promoting a text message plan that costs each month plus five cents per text.

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In elementary algebra, linear equations are algebraic equations in which both sides of the equation are polynomials or monomials of the first degree - i.e.

each term does not have any variables to a power other than one.

These "real life" systems can have dozens or hundreds of variables, or more.

In algebra, though, you'll only work with the simple (and graphable) two-variable linear case.-plane (called the "feasibility region").

In "real life", linear programming is part of a very important area of mathematics called "optimization techniques".

This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources.I mean, I've ridden trains between Chicago and New York, but I've never plotted when my train will pass another. To multiply with a percent, we convert it to a decimal. If you want to try the new plan and spend only each month, how many texts can you send? In this lesson, we'll not only practice solving problems that can be translated into linear equations, we'll also focus on problems you may encounter in your life - problems not involving trains passing each other. If we solve for x by subtracting 35 from both sides, we get x = 37. They can be a bit more complex, like this: 15 less than four times a number is 57. So this is the amount of time she's just gonna spend reading.And so the amount she spends on homework plus the amount she spends on reading need to add up to 19 hours.A train leaves Chicago at 7 a.m., traveling at 70 mph to New York, which is 800 miles away. We're going to ignore the questionable judgment he displays in loaning money to family. You can test out of the first two years of college and save thousands off your degree.Another train leaves New York at the same time, traveling on a parallel track to Chicago at 85 mph. The question is: why do we care so much about trains? If he loans you 0, how much interest will you need to pay? You decide that you want to be better about saving money. Anyone can earn credit-by-exam regardless of age or education level.So which of these choices are what I just wrote over here?So let's see, they have the 19 on the other side but you see they have 2 1/2 C minus 6 1/2, no that's not this right over here.Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions.A typical example would be taking the limitations of materials and labor, and then determining the "best" production levels for maximal profits under those conditions.

• ###### Linear Functions Problems with Solutions -

Linear Functions Problems with Solutions. Linear functions are highly used throughout mathematics and are therefore important to understand. A set of problems involving linear functions, along with detailed solutions, are presented. The problems are designed with emphasis on the meaning of the slope and the y intercept.…

• ###### Problem solving using Linear Equations - Video & Lesson.

From sale prices to trip distances, many real life problems can be solved using linear equations. In this lesson, we'll practice translating word.…

This is a system of linear equations with two variables, which can be found in Tutorial 19 Solving Systems of Linear Equations in Two Variable. Simplify if needed. We can simplify this by dividing both sides of equation 1 by 2 and equation 2 by 2.5 getting rid of the and decimals at the same time…

• ###### Systems of Linear Equations and Problem Solving - West.

Jul 10, 2011. Use Polya's four step process to solve various problems involving systems of linear equations in both two and three variables.…

• ###### Linear Equation Calculator - Symbolab

Basic Linear Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode…

• ###### Introduction to Linear Programming and Optimization in.

Feb 28, 2017. Linear programming LP is one of the simplest ways to perform optimization. It helps you solve some very complex optimization problems by.…