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A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true.
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.
As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more. So, it'll take you just over 11 weeks to get that bike. If you played 3 games and paid $3 each for shoes, how much did you pay per game? We looked at simple examples, where the problem describes a number in terms of details about it, like the sum of twice a number and 52 is 174.
Plus, get practice tests, quizzes, and personalized coaching to help you succeed. If we want to save $400, then our equation is 35w = 400. After you get the bike, you decide to have some fun. Then, we looked at problems that involve real-life scenarios, from loaning money to bowling.
Hopefully, the passengers will have finished their linear equation word problems and look up in time to wave.
So, they'll meet 5 hours into their respective trips.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.However, in some areas of mathematics the convention is to reserve some variables as known and others as unknown.When writing polynomials, the coefficients are usually taken to be known and the indeterminates to be unknown, but depending on the problem, all variables may assume either role.Solving an equation numerically means that only numbers represented explicitly as numerals (not as an expression involving variables), are admitted as solutions.Solving an equation symbolically means that expressions that may contain known variables or possibly also variables not in the original equation are admitted as solutions. Note that the distinction between known variables and unknown variables is made in the statement of the problem, rather than the equation. 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. For solutions of constraint satisfaction problems, see Constraint satisfaction problem § Resolution.For solutions of mathematical optimization problems, see Feasible solution.