Lesson 2 8 solving system of equations by substitution
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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

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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.


Lesson 2 8 solving system of equations by substitution

  • 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.


Lesson 2 8 solving system of equations by substitution

  • 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.


Lesson 2 8 solving system of equations by substitution

  • 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.


Lesson 2 8 solving system of equations by substitution

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.


You try

You try!

1)

2)


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