Lesson 6: 1-6 Solving Systems of Equations

How can you tell by looking at a graph whether or not there is a solution to a system of linear equations? By looking at the equations?
In a real world problem involving a system of linear equations, what questions can you ask yourself to help make sense of the problem?
How can you check your answers?

System of equations
consistent
inconsistent
independent
dependent
substitution method
eliminations method

A.CED.2 Create equations in tow or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales
A.CED.3 Represent constraints by equations or inequalities, and by system s of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context.
A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x): find the solutions approximately. Include cases where f(x) and g(x) are linear, polynomial, rational, absolute value, exponential and log functions.

SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8; systems: 4-3-16,1-3-18,1-3-9,2-3-2,8-3-18,6-4-11,7-3-3,1-3-11,7-4-11,1-4-19,8-3-10,2-4-29,2-3-20,3-3-9; writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19; inequalities: 5-4-13,7-4-5,4-4-19,8-3-6,1-4-28,5-3-7,6-3-14; graphing: 6-3-5; total unit: 2-3-9

If the coefficients for one of the variables in the two equations are already the same or opposite, that variable can be easily eliminated by subtracting or adding the given equations. If this is not the case, it may be a better choice to use the substitution method. Substitution and elimination can each be used to solve a system of equations.

Libby borrowed $450 to start a lawn-mowing business. She charges $35 per lawn and incurs $8 in operating costs per lawn. A system of equations can be used to determine the break-even point. The break-even point is the point at which the cost become equal.

If students have trouble with vocabulary, have them create a set of flashcards. On one side is the vocab word, on the other side is a picture or definition.

Use McGraw Hill Materials

Use McGraw Hill Materials.