System of Equations Determine the Best Method Objective

System of Equations Determine the Best Method Objective: Students will determine the best method for solving systems of equations. S. Calahan March 2008

Best time to use Graphing § Used to estimate the solution, since graphing usually does not give an exact solution.

Substitution § Used if one of the variables in either equation has a coefficient of 1 or -1. § y = 2 x + 2 and 2 x + y = 11

Substitute and solve 2 x + (2 x + 2) = 11 3 x + 2 = 11 y = 2 x + 2 -2 -2 y = 2(3) + 2 3 x = 9 y=8 x=3 (3, 8)

Elimination using Addition § Use if one of the variables has opposite coefficients in the two equations. § 9 x - 8 y = 42 and 4 x + 8 y = -16

Solve § 9 x – 8 y = 42 9(2) – 8 y = 42 + 4 x + 8 y = -16 18 – 8 y = 42 13 x = 26 -18 x=2 -8 y = 24 (2, -3) y = -3

Elimination using subtraction § Use if one of the variables has the same coefficient in the two equations. § 6 x – y = 9 and 6 x – y = 11

Solve § 6 x – y = 9 - 6 x – y = -11 0 = -2 No solution

Elimination using Multiplication § Use if none of the coefficients are 1 or -1 and neither of the variables can be eliminated by simply adding or subtracting the equations. § 3 x – 4 y = -10 and 5 x + 8 y = -2

Solve § 3 x – 4 y = -10 Multiply by 2 5 x + 8 y = -2 +6 x – 8 y = -20 3(-2) + 4 y = -10 11 x = -22 -6 + 4 y = -10 x = -2 +6 +6 4 y = -4 (-2, -1) y = -1