Solving linear equations in two
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Solving linear equations in two

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    Solving linear equations in two Solving linear equations in two Presentation Transcript

    • 2010
      • A first degree equation is called a linear equation in two variables if it contains two distinct variables.
      • 1. Arbitrarily select some points that satisfy the equation.
      • 2. Plot the points in a coordinate plane.
      • 3. Draw the line passing through these points. This is the graph of the equation.
      • Graph y = 2x + 3.
      • Plotting the x-intercept and y-intercept of a graph and drawing a line through them is called the intercept method of graphing a linear equation.
      • Graph y = 2x + 4.
      • Set of two or more equations is called a system of equations .
      • Consider the following system of equations:
      • y – 2x = –6
      • y + x = –3
      • To solve the system, we can first graph each equation.
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      • In order to solve a system of equations we can write the equations in a way that eliminates one of the unknowns. Then the remaining equality will be in one unknown, and we can solve this easily. This method is called the elimination method.
      • 1. Write the given equations in the form Ax + By = C.
      • 2. Take one equation. Make the coefficient of the variable which you want to eliminate the additive inverse of the same variable in the other equation.
      • 3. Add the resulting equations to eliminate your chosen variable.
      • 4. Solve the resulting equation in one unknown.
      • 5. Find the other variable by substituting this solution into either original equation.
      • 6. Check your result.
      • Another method for solving systems of equations is the substitution method.
      • 1. Solve one of the equations for one variable in terms of the other variable.
      • 2. Substitute the resulting expression into the other equation and solve.
      • 3. Find the other variable by substituting the result of step 2 into either original equation.
      • 4. Check your result.