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Chapter 4 Section 1

Chapter 4 Section 1. Systems of Equations in two Variables. So, what constitutes a solution? Notice that we have 2 variables and as such we will need 2 values to be a solution. Hence the solutions are ordered pairs. For example, is (1, 2) a solution to the given system?. Your Turn.

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Chapter 4 Section 1

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  1. Chapter 4 Section 1 Systems of Equations in two Variables

  2. So, what constitutes a solution? Notice that we have 2 variables and as such we will need 2 values to be a solution. Hence the solutions are ordered pairs. • For example, is (1, 2) a solution to the given system?

  3. Your Turn • Determine if any of the given ordered pairs are solutions to the given system of equations.(0, 3), (1, 5), (2, 7);

  4. How Many Solutions Can You Have? • There were three possible situations that we could get from a system.

  5. One Solution • One Solution at a single point. We say the system is independent.

  6. Infinite Solutions • The equations have the same graph and has an infinite number of solutions. We say the system is dependent.

  7. No Solution • When you solve graphically, you’ll get parallel lines. There are no solutions. Since it is two different equations, it is still independent.

  8. Number of Solutions

  9. For All Problems in Section 4.1 • Solve both equations for y. That is, write the equation in y = mx + b slope-intercept form. • Put the equations into Y1 and Y2. • Graph the equations and adjust the WINDOW until you see the point of intersection. • Use the INTERSECT routine in the calculator to find the point of intersection. • Make a reasonable sketch of the graph and label your solution on the graph. Use a rule to draw all lines.

  10. Problem Solving • Analyze the problem. • Define your variables and form a system of equations. • Solve the system. • Check the solution. • State the conclusion.

  11. Modeling the Real World • A standard tennis court used for doubles has a perimeter of 228ft. The width is given to be 42ft less than the width. Translate into a system of equations.

  12. Green Diamond Can either convert logs into lumber of plywood. In a given day the mill turns out 42 units of plywood and lumber. It makes a profit of $2500 on a unit of lumber and $4000 on a unit of plywood. How many units of each type were produced if they sold all 42 units and made a profit of $124,500?

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