Solving linear equations in two

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Solving linear equations in two

  1. 1. 2010
  2. 2. <ul><li>A first degree equation is called a linear equation in two variables if it contains two distinct variables. </li></ul>
  3. 3. <ul><li>1. Arbitrarily select some points that satisfy the equation. </li></ul><ul><li>2. Plot the points in a coordinate plane. </li></ul><ul><li>3. Draw the line passing through these points. This is the graph of the equation. </li></ul>
  4. 4. <ul><li>Graph y = 2x + 3. </li></ul>
  5. 5. <ul><li>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. </li></ul>
  6. 6. <ul><li>Graph y = 2x + 4. </li></ul>
  7. 7. <ul><li>Set of two or more equations is called a system of equations . </li></ul>
  8. 8. <ul><li>Consider the following system of equations: </li></ul><ul><li>y – 2x = –6 </li></ul><ul><li>y + x = –3 </li></ul><ul><li>To solve the system, we can first graph each equation. </li></ul>
  9. 12. <ul><li>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. </li></ul>
  10. 13. <ul><li>1. Write the given equations in the form Ax + By = C. </li></ul><ul><li>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. </li></ul><ul><li>3. Add the resulting equations to eliminate your chosen variable. </li></ul><ul><li>4. Solve the resulting equation in one unknown. </li></ul><ul><li>5. Find the other variable by substituting this solution into either original equation. </li></ul><ul><li>6. Check your result. </li></ul>
  11. 14. <ul><li>Another method for solving systems of equations is the substitution method. </li></ul>
  12. 15. <ul><li>1. Solve one of the equations for one variable in terms of the other variable. </li></ul><ul><li>2. Substitute the resulting expression into the other equation and solve. </li></ul><ul><li>3. Find the other variable by substituting the result of step 2 into either original equation. </li></ul><ul><li>4. Check your result. </li></ul>

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