In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.When seeking a solution, one or more free variables are designated as unknowns.
The second train is going 85 mph for t time, or 85t. In other words, when do the two distances add up to the total distance, 800 miles. Now, we divide both sides by 160, and we get t = 5.
The first train is traveling at a rate of 75 mph, so the distance it covers in t time is 75t.
A wording such as "an equation in x and y", or "solve for x and y", implies that the unknowns are as indicated: in these cases x and y. Note that the set of solutions can be the empty set (there are no solutions), a singleton (there is exactly one solution), finite, or infinite (there are infinitely many solutions).
For example, an equation such as One particular solution is x = 0, y = 0, z = 0.
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Try it risk-free From sale prices to trip distances, many real life problems can be solved using linear equations. Let's say you're a little short on cash and need a loan. You've been averaging way more than that, so maybe this isn't a great plan. If you can save each week, how many weeks will it take you to get the bike? We focused on defining the variable, or the unknown quantity, in terms of what is known, then solving for the variable.
In this lesson, we'll practice translating word problems into linear equations, then solving the problems. Let's take that knowledge and look at some real life situations. Your cousin agrees to loan you money, and you agree that you'll repay him in full plus 4% interest. But, then you get a new job, and suddenly you have some extra cash. Oh, and we solved the dreaded algebra train problem. You'll be able to translate word problems into linear equations and solve those equations after watching this video lesson. We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities.
As a reminder, a is just an algebraic expression that represents a line.
These equations typically have one variable and look like 3x = 9 or y 4 = 10.