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Solving Systems of Linear Equations by Graphing

This guide explores how to solve systems of linear equations by graphing. A system is defined by two or more linear equations, for instance, 5x + 6y = 14 and 2x + 5y = 3. We illustrate how to find solutions graphically by checking specific points against the equations. Examples include determining if (1, 2) or (-4, 7) is the solution for a given system. Additionally, we discuss cases of parallel lines with no solution and coinciding lines with infinite solutions. Understanding consistent and inconsistent systems is key.

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Solving Systems of Linear Equations by Graphing

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  1. 7.1 System of Equations Solve by graphing

  2. A system of linear equations consists of two or more linear equations: • For example: 5x + 6y = 14 2x + 5y = 3

  3. 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 ? -27Is 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 Solution of the system

  4. 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)

  5. 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

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

  7. A system of equations is consistent if they have at least one solution • A system of equation is inconsistent if they have no solution

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