4 1 solving linear systems by graphing
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This document discusses solving linear systems of equations by graphing. A linear system is a set of two or more linear equations where a solution is an ordered pair that satisfies both equations. Graphing the equations on the same grid allows you to find the point of intersection, which is the solution. Systems can have one solution, infinitely many solutions if the lines are the same, or no solution if the lines are parallel.
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4 1 solving linear systems by graphing
- 1. 4-1 SOLVING LINEAR SYSTEMS BY GRAPHING
- 2. WHAT IS A LINEAR SYSTEM? A set of two or more linear equations. A solution is an ordered pair (x, y) that makes BOTH equations true. Happens graphs at the intersection of the
- 3. CHECKING SOLUTIONS Example: Is 3x x Is (2, 2) a solution of the system? 2y 2y 2 6 (0, -1) a solution?
- 4. SOLVING BY GRAPHING 1. 2. 3. Graph each equation on the same grid Estimate the point of intersection Check solution in original system (BOTH equations!)
- 5. EXAMPLE Solve y = 2x + 5 y = -4x – 1
- 6. YOUR TURN! Solve y=x–1 y = -x + 3
- 7. MANY SOLUTIONS When will a system have infinitely many solutions? When both equations are the same line! Example: y = -5x – 2 5x + y = -2
- 8. NO SOLUTIONS When will a system have no solution? When the lines are parallel! Example: y = 3x + 1 y = 3x – 5
- 9. SUMMARY Lines intersect at one point. One Solution Both are same line. Infinitely Many Solutions Two parallel lines. No Solution