 # 3.1 System of Equations Solve by graphing. Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7)

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3.1 System of Equations Solve by graphing

Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7) Is 1 + 2 ? 3Is -4 + 7 ? 3 3 = 3 yes 3 = 3 yes Is 5·1-2 ? -27 Is 5·(-4)-7 ? -27 5 - 2 ? -27 -20 – 7 ? -27 -3 = -27 no -27 = -27 yes So (1,2) is not the So (-4,7) is the solution Solutionof the system

Solve by Graphing Ex 1) y – x = 1 y + x = 3 y = x + 1 y = -x + 3 Therefore the solution of this system is (1,2) (1,2)

Solve by Graphing Ex 1) y = -3x + 5 y = -3x - 2 The lines are parallel, so there is no solution for this system of equations

Solve by Graphing Ex 1) 3y – 2x = 6 -12y + 8x = -24 3y = 2x + 6 -12y = -8x - 24 y = 2/3 x + 2 There are infinite numbers of solution because the lines are coinciding

A system of equations is consistent if they have at least one solution A system of equation is inconsistent if they have no solution A system of equations is dependent if it has many solutions A system of equations is independent if it has one solution or no solutions ***When an equation in a system can be obtained by multiplying both sides of another equation by a constant, the two equations are said to be dependent

Example Y = -2 X = 2 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: (2, -2), consistent, independent

Example 6x – 2y = 2 9x – 3y = 1 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: No solution; inconsistent, independent

Example Y = 3 - x 2x +2y = 6 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: Infinite many solutions; consistent, dependent

Example Y = 4 - x Y = x - 4 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: (4,0) consistent, independent

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