# One solution no solution infinite solutions example

CCSS.Math.Content.8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Model and solve equations using algebra tiles (Eighth grade - U.2) Write and solve equations that represent diagrams (Eighth grade - U.3)

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Example: 3x + 2y = 19; x + y = 8; We can start with any equation and any variable. Let's use the second equation and the variable "y" (it looks the simplest equation). Write one of the equations so it is in the style "variable = ...": We can subtract x from both sides of x + y = 8 to get y = 8 − x. Now our equations look like this: 3x + 2y = 19; y = 8 − x

Many different kinds of solutions exist. For example, a solute can be a gas, a liquid or a solid. Solvents can also be gases, liquids or solids. The following figures show the microscopic behavior of several different kinds of solutions. Note that in each case, the solute particles are uniformly distributed among the solvent particles. The pair of equations has a unique solution. The pair of linear equations is consistent. Lines parallel to each other => No solutions. The pair of linear equations is inconsistent. Coincident lines => Infinite number of solutions. The pair of linear equations is consistent and dependent.

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