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Systems of Linear Equations: Graphing and Solutions

Learn about systems of linear equations in two variables, how to graph them, and find their solutions. Determine if given points are solutions and solve systems using different methods.

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Systems of Linear Equations: Graphing and Solutions

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  1. Chapter 3 Section 1 Systems of Linear Equations in Two Variables All graphs need to be done on graph paper. Four, five squares to the inch is the best. One unit = one square

  2. Solutions • One ordered pair • The two lines intersect at one point. • Consistent system • No solution • The two lines are parallel. • Dependent system • Infinitely many solutions • The two lines are identical. • Same line • Inconsistent system.

  3. System of Linear Equations • Two or more linear equations • Solution • The ordered pair that satisfies both equations. • When graphing, the point where the two lines intersect.

  4. Writing the Solution If two line cross at (3,4) Solution: • Solution: x = 3 and y = 4 • The intersection is (3, 4).

  5. Systems of Equations and Their Solutions • Is (7, 2) a solution to the system? • Is (-3, - 4) a solution to the system?

  6. Solve the system by graphing c) d) Note: Find the point of intersection.

  7. Solve the system by substitution e) f) Note: Find the point of intersection.

  8. Solve the system by addition g) h)

  9. Solve the system i)

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