solution, infinitely no solution: An example of a linear equation in one variable with no solutions is x + many solutions, or no 1 = + 2. x Show which solutions. of these possibilities is the case by successively transforming the given equation into simpler equivalent equation: Equations with the same value are equivalent, for example: 2 forms, until an + 3 = 11 6 is equivalent to 5 = 5 OR y +3 = 5 is equivalent to y = 2. − equivalent equation of the form of = = or = x a, a a, a b results (a and b are different numbers). See the skills and distributive property: The distributive property states that for all numbers a, b, and knowledge that are c, a(b + c) = ab + ac stated in the Standard. 8.EE.C.7b: linear equations Examples are a(b + c) = ab + ac and 3x(x+4) = 3x(x) + 3x(4) with rational number = 3x2+12x coefficients, including equations whose collecting like terms: This process is also known as like terms. “combining” solutions require Example: 2x + 3 + 5x = 7x +3 expanding expressions using the distributive property and collecting like terms. 8.EE.C.8: Analyze and solve pairs of
solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form of x = a, a = a, or a = b results (a and b are different numbers). 8.EE.C.7b: linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. See the skills and knowledge that are stated in the Standard. no solution: An example of a linear equation in one variable with no solutions is x + 1 = x + 2. equivalent equation: Equations with the same value are equivalent, for example: 2 + 3 = 11 − 6 is equivalent to 5 = 5 OR y +3 = 5 is equivalent to y = 2. distributive property: The distributive property states that for all numbers a, b, and c, a(b + c) = ab + ac Examples are a(b + c) = ab + ac and 3x(x+4) = 3x(x) + 3x(4) = 3x2+12x collecting like terms: This process is also known as “combining” like terms. Example: 2x + 3 + 5x = 7x +3 8.EE.C.8: Analyze and solve pairs of
Unit_8_EE_C_7_8Solve_Linear_Equations_Simultaneous_Linear_Equations_Final.docx