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MPM2D – Linear Systems – Analyzing Linear Systems

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kelii
12 diapositives · 500 Views · Jul 26, 2014

MPM2D – Linear Systems – Analyzing Linear Systems. Single Equations and Systems of Equations We can find a single solution for an equation with 1 variable: We cannot find a single solution if we have an equation with 2 variables:

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  1. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations We can find a single solution for an equation with 1 variable: We cannot find a single solution if we have an equation with 2 variables: This is a linear equation with an infinite number of solutions, such as (0, 4) , (1, 6) , and (-2, 0)

  2. However, 2 linear relations could intersect at a single point, which might provide the solution that is needed. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations (5, -2)

  3. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Is (-1, 11) a solution to the following equation? Substitute into the equation to do a left side/right side check: Since L.S. = R.S., (-1, 11) is a solution to

  4. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Which of the following ordered pairs satisfy the equation ? (3, 5) , (1.5, -1.5) , (0.5, -2.5) , (2.5, 2.5)

  5. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Which of the following ordered pairs satisfy the equation ? (3, 5) , (1.5, -1.5) , (0.5, -2.5) , (2.5, 2.5)

  6. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Complete each ordered pair below, so that it satisfies a) (2, ) b) ( , 8) c) ( , -13) d) (-2, )

  7. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Complete each ordered pair below, so that it satisfies a) (2, 5) b) ( , 8) c) ( , -13) d) (-2, )

  8. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Complete each ordered pair below, so that it satisfies a) (2, 5) b) (3, 8) c) ( , -13) d) (-2, )

  9. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Complete each ordered pair below, so that it satisfies a) (2, 5) b) (3, 8) c) (-4, -13) d) (-2, )

  10. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Complete each ordered pair below, so that it satisfies a) (2, 5) b) (3, 8) c) (-4, -13) d) (-2, -7)

  11. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Two or more equations being considered together is called a system of equations. Do a left side/right side check to verify that (5, 2) is the solution to the following system of equations: For ; For ; Therefore, (5, 2) is the solution to the system.

  12. The solution to the previous system of equations can be modelled on a graph. MPM2D – Linear Systems – Analyzing Linear Systems Single Equations and Systems of Equations Notice that (5, 2) is the only point that lies on both lines.