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Lesson 2.8 Solving system of equations by substitution . ‘In Common’ Ballad: http://youtu.be/Br7qn4yLf-I ‘All I do is solve’ Rap: http://youtu.be/1qHTmxlaZWQ. Key concepts.

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lesson 2 8 solving system of equations by substitution

Lesson 2.8Solving system of equations by substitution

‘In Common’ Ballad: http://youtu.be/Br7qn4yLf-I

‘All I do is solve’ Rap: http://youtu.be/1qHTmxlaZWQ

key concepts
Key concepts
  • There are various methods to solving a system of equations. A few days ago we looked at the graphing method. Today we are going to look at the substitution method.
  • The substitution method involves solving one of the equations for one of the variables and substituting that into the other equation.
  • Solutions to systems are written as an ordered pair, (x,y). This is where the lines would cross if graphed.
key concepts continued
Key concepts continued
  • If the resulting solution is a true statement, such as 9 = 9, then the system has an infinite number of solutions. This is where the lines would coincide if graphed.
  • If the result is an untrue statement, such as 4 = 9, then the system has no solutions. This is where lines would be parallel if graphed.
  • Check your answer by substituting the x and y values back into the original equations. If the answer is correct, the equations will result in true statements.
steps for substitution method
Steps for substitution method
  • Step 1: Solve one of the equations for one of its variables.
  • Step 2: Substitute the expression from step 1 into the other equation.
  • Step 3: Solve the equation from step 2 for the other variable.
  • Step 4: Substitute the value from step 3 into the revised equation from step 1 (or either of the original equations) and solve for the other variable.
example 1
Example 1:
  • Step 1: Solve one of the equations for one of its variables.
    • It doesn’t matter which equation you choose, nor does it matter which variable you solve for.
    • Let’s solve for the variable y.

Isolate y by subtracting x from both sides.

slide6

Step 2: Substitute into the other equation, .

    • It helps to place parentheses around the expression you are substituting.
  • Step 3: Solve the equation from step 2 for the other variable.

Second equation of the system.

Substitute for y.

Distribute the negative over

Simplify.

Add 2 to both sides.

Divide both sides by 2.

slide7

Step 4: Substitute the value, (), into the revised equation from step 1 (or either of the original equations) and solve for the other variable.

  • The solution to the system of equations is (). If graphed, the lines would cross at ().

Revised equation from step 1.

Substitute for .

Simplify.

example 2
Example 2:
  • Step 1: Solve one of the equations for one of its variables.
    • It doesn’t matter which equation you choose, nor does it matter which variable you solve for.
    • Let’s solve for the variable x.

Isolate by adding to both sides.

slide9

Step 2: Substitute into the other equation, .

    • It helps to place parentheses around the expression you are substituting.
  • Step 3: Solve the equation from step 2 for the other variable.

Second equation of the system.

Substitute for .

Distribute the 4 through

Simplify.

Add 12 to both sides.

Divide both sides by 5.

slide10

Revised equation from step 1.

  • Step 4: Substitute the value, (), into the revised equation from step 1 (or either of the original equations) and solve for the other variable.
  • The solution to the system of equations is (). If graphed, the lines would cross at ().

Substitute for y.

Simplify.