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Transcript
Section 7-1 Solve Systems by Graphing SPI 23D: select the system of equations that could be used to solve a given real-world problem Objective: • Solve systems of linear equations by graphing • Slope-intercept form of a linear equation: y = mx + b • Standard form of a linear equation: Ax + By = C Systems of Linear Equations: • two or more linear equations together Solving Systems of Equations: • means finding a solution to both equations (an ordered pair) that makes both equations true Recall Graphing Slope-Intercept Form of a Linear Equation Graph y = - 1 x – 2 2 Y 1. Plot y-intercept 2. From known point, plot slope. 3. Connect the 2 points with a line. 0 X Recall Graphing Standard Form of a Linear Equation Graph the equation -5x – 2y = 10. Step 1. Find the x-intercept. -5x – 2(0) = 10 -5x = 10 x = -2 (-2, 0) Step 2. Find the y-intercept. -5(0) – 2y = 10 -2y = 10 y = -5 (0, -5) Step 3. Plot both ordered pair and draw the line. Solve Systems of Equations Three Methods of solving Systems of Equations: • Solve by Graphing • Solve by Substitution • Solve by Elimination Solve a System of Equations by Graphing Solve by graphing. y=x+5 y = -4x 1. Graph the equations on the same coordinate plane. 0 2. Write the ordered pair where the lines intersect. (-1, 4) Solution that will make both equations true. Solve Systems of Equations Life Science. You are testing two fertilizers on a plant which grow under identical conditions. The equation H(d) = 4d + 6 models the growth rate of the first plant and the equation H(d) = 2d + 10 models the growth rate of the second plant. In the equations, d represents the number of days it takes the plants to grow a certain height, H(d). 1. Model the equations by graphing on the same coordinate plane. 2. After how many days will the plants be the same height? 2 days 3. What will their height be? 14 cm Number of Solutions to a System of Equations A System of Equations can have: • One Solution • No Solution • Infinitely Many Solutions One Solution • different slopes • lines intersect No Solution Infinitely Many • same slope • same slope • lines are parallel • same y-intercept • different y-intercepts