SP

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- MATH
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- this lesson: learning how to solve system of linear equations using substitution method
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- Why substitution
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- It gives the exact result for both variables. It is easier to understand the faster method of solving equations.
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- Steps 1. Isolate one of the variables 2. Substitute the expression for the other equation 3. Solve the equation found. 4. Substitute the result of the variable into the other equation 5. Solve the equation. 6. Write the answer is a ordered pair like this (x, y) if needed
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- here is an example of solving a equation: Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30
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- Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30 step one: The coefficient of x in Equation 2 is 1. So first we make x to be alone on one side. like this
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- x = 30 - 8y
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- Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30 step 2: substitute this expression for x in Equation 1 and solve for y 2(30 - 8y) + 4y = 12 60 - 16y + 4y = 12 -12y = -48
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- Multiply out bracket Combine like terms Divide both sides by -12 to solve for y
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- y = 4
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- Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30 step 3: substitute the solution for y into the expression for x x = 30 - 8(4) = -2 x = -2
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- Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30 step 4: Write the answer is a ordered pair
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- (-2, 4)
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- Another one equation 1: 3x + y = 13 equation 2: 5x -2y = 7 step 1: The coefficient of y in Equation 1 is 1. So first we make y to be alone on one side like this
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- y = 13 - 3x
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- equation 1: 3x + y = 13 equation 2: 5x -2y = 7 step 2: substitute this expression for y in Equation 2 and solve for x 5x - 2(13 - 3x) = 7 5x - 26 + 6x = 7 11x = 33
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- Multiply out bracket Combine like terms Divide both sides by 11 to solve for x
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- x = 3
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- equation 1: 3x + y = 13 equation 2: 5x -2y = 7 step 3: substitute the solution for x into the expression for y y = 13 - 3(3) = 4 y = 4
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- equation 1: 3x + y = 13 equation 2: 5x -2y = 7 step 4: Write the answer is a ordered pair
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- (3, 4)
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- try some yourself
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- Easy: x + y = 5 3x + y = 11
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- the answer is (3,2)is
- 01:48
- hard x + 3y = 10 3y = 10 - x
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- try this
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- Here a little hint the answer will be in a fraction
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- the answer (11, -1/3)
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- that it for this lesson