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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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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
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.
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.
Writing the Solution If two line cross at (3,4) Solution: • Solution: x = 3 and y = 4 • The intersection is (3, 4).
Systems of Equations and Their Solutions • Is (7, 2) a solution to the system? • Is (-3, - 4) a solution to the system?
Solve the system by graphing c) d) Note: Find the point of intersection.
Solve the system by substitution e) f) Note: Find the point of intersection.