8.AT.B: Make sense of and solve equations, inequalities, and systems of equations

Make sense of and solve equations, inequalities, and systems of equations

8.AT.B.3Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solution. Justify each example by showing how it can be rewritten in an equivalent equation in the form x=a, a=a, or a=b (where a and b are different rational numbers) and explaining what this form reveals about the solution. b. Solve linear equations in one variable with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combing like terms.8.AT.B.4Solve linear inequalities in one variable. a. Solve inequalities including those requiring the use of the distributive property and combining like terms. b. Represent the solution set on a number line and describe the set of possible values in the context of the problem.8.AT.B.5Analyze and solve systems of two linear equations in two variables. a. Interpret the solution to a system of two linear equations as the point where their graphs intersect and verify that the coordinates of the intersection satisfy both equations. b. Solve systems of two linear equations by graphing and substitution. When using graphing, find an approximate or exact solution depending on the precision of the graph. Select a method strategically based on the structure of the system or the context of the problem and explain why the method is appropriate. c. Use structure to determine when a system has no solution, one solution, or infinitely many solutions and justify the conclusion. d. Model and solve contextual problems using systems of two linear equations.

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