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Project 1

Project 1

Published on 5 December 2022
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Transcript
00:00
MATH
00:05
this lesson: learning how to solve system of linear equations using substitution method
00:10
Why substitution
00:11
It gives the exact result for both variables. It is easier to understand the faster method of solving equations.
00:17
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
00:25
here is an example of solving a equation: Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30
00:30
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
00:34
x = 30 - 8y
00:40
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
00:43
Multiply out bracket Combine like terms Divide both sides by -12 to solve for y
00:45
y = 4
00:47
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
00:53
Equation 1: 2x + 4y = 12 Equation 2: x + 8y = 30 step 4:  Write the answer is a ordered pair
00:56
(-2, 4)
01:03
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
01:08
y = 13 - 3x
01:11
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
01:14
Multiply out bracket Combine like terms Divide both sides by 11 to solve for x
01:16
x = 3
01:21
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
01:28
equation 1: 3x + y = 13 equation 2: 5x -2y = 7 step 4: Write the answer is a ordered pair
01:31
(3, 4)
01:35
try some yourself
01:37
Easy:  x + y = 5 3x + y = 11
01:45
the answer is (3,2)is 
01:48
hard x + 3y = 10 3y = 10 - x
01:49
try this
01:51
Here a little hint the answer will be in a fraction
01:57
the answer (11, -1/3)
01:59
that it for this lesson