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5.3 Solving Systems of Linear Equations by Elimination

5.3 Solving Systems of Linear Equations by Elimination. How can you use elimination to solve a system of linear equations? Students will be able to solve a system of linear equations by elimination. Students will be able to solve a system of linear equations by elimination.

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5.3 Solving Systems of Linear Equations by Elimination

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  1. 5.3 Solving Systems of Linear Equations by Elimination How can you use elimination to solve a system of linear equations? Students will be able to solve a system of linear equations by elimination.

  2. Students will be able to solve a system of linear equations by elimination. Solving a System of Linear Equations by Elimination Step 1Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same or opposite coefficients. Step 2Add or subtract the equations to eliminate one of the variables. Step 3Solve the resulting equation. Step 4 Substitute the value from Step 3 into one of the original equations and solve the other variable. Step 5 Check your answer in the other equation you did not use in Step 4.

  3. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Because the coefficients of the y-terms are opposites, you do not need to multiply either equation by a constant. Step 2Add the equations. Equation 1 Equation 2 Step 3 Solve for x.

  4. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Because the coefficients of the y-terms are opposites, you do not need to multiply either equation by a constant. Step 2Add the equations. Equation 1 Equation 2 Step 3 Solve for x. Step 4 Substitute 0 for x in one of the original equations and solve for y. Equation 1 The solution is . Step 5 Check your solution in the other equation. Equation 2

  5. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 2 by -2 so that the coefficients of the x-terms are opposites. Step 2Add the equations. Equation 1 Revised Equation 2 Step 3 Solve for y.

  6. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 2 by -2 so that the coefficients of the x-terms are opposites. Step 2Add the equations. Equation 1 Equation 2 Step 3 Solve for y. Step 4 Substitute -3 for y in one of the original equations and solve for x. Equation 1 The solution is . Step 5 Check your solution in the other equation. Equation 2

  7. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 1 by -2 so that the coefficients of the x-terms are opposites. Step 2Add the equations. Revised Equation 1 Equation 2 The equation is always true. So, the solutions are all the points on the line . The system of linear equations has infinitely many solutions. Because the lines are the same line!

  8. Students will be able to solve a system of linear equations by elimination. Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 1 by 4 and Equation 2 by -6 so that the coefficients of the x-terms are opposites. Step 2Add the equations. Revised Equation 1 Revised Equation 2 The equation is never true. So, the system of linear equations has no solution. Because the lines are parallel!

  9. So let’s review! • Students will be able to solve a system of linear equations by substitution. • Step 1 Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same or opposite coefficients. • Step 2 Add or subtract the equations to eliminate one of the variables. • Step 3 Solve the resulting equation. • Step 4 Substitute the value from Step 3 into one of the original equations and solve the other variable. • Step 5 Check your answer in the other equation you did not use in Step 4. • Remember! • If the equation is never true, there is no solution. • If the equation is always true, there are infinitely many solutions.

  10. You Try!! Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 1 by 3 and Equation 2 by 2 so that the coefficients of the y-terms are opposites. Step 2Add the equations. Revised Equation 1 Revised Equation 2 Step 3 Solve for x.

  11. You Try!! Solve the system of linear equations by elimination. Equation 1 Equation 2 Step 1Multiply Equation 1 by 3 and Equation 2 by 2 so that the coefficients of the y-terms are opposites. Step 2Add the equations. Revised Equation 1 Revised Equation 2 Step 3 Solve for x. Step 4 Substitute 5 for x in one of the original equations and solve for y. Equation 2 The solution is . Step 5 Check your solution in the other equation. Equation 1

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