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Greekfreak
13.10.2020 •
Mathematics
3x + 4y -z = 1
3x-y-4z=-3
x+3y-3z = 9
*Use Elimination to solve*
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Ответ:
y = 2
z = -2
Step-by-step explanation:
When solving by elimination:
• Subtract equations that have a variable with the same coefficient
• Add equations that have a variable with the same coefficient but different sign
1. Label your equations
3x + 4y - z = 1 [1]
3x - y - 4z = -3 [2]
x + 3y - 3z = 9 [3]
2. Add/Subtract equations
[1] - [2], both have “3x”
3x + 4y - z = 1 [1]
3x - y - 4z = -3 [2]
————————
5y + 3z = 4 [4]
Multiply [3] by 3
=> 3x + 9y - 9z = 27 [5]
[5] - [2], both have “3x”
3x + 9y - 9z = 27 [5]
3x - y - 4z = -3 [2]
—————————-
10y - 5z = 30
2y - z = 6
-z = 6 - 2y
z = 2y - 6 [6]
Substitute [6] into [4]
5y + 3z = 4 [4]
5y + 3(2y - 6) = 4
5y + 6y - 18 = 4
11y - 18 = 4
11y = 22
y = 2 ⭐️
Substitute y = 2 into [6]
z = 2y - 6 [6]
z = 2(2) - 6
z = 4 - 6
z = -2 ⭐️
Substitute y = 2, z = -2 into [3]
x + 3y - 3z = 9 [3]
x + 3(2) - 3(-2) = 9
x + 6 + 6 = 9
x + 12 = 9
x = -3 ⭐️
Therefore, x = -3, y = 2 and z = -2.
Ответ:
145,146,147
Step-by-step explanation:
Let x be the first number
x+1 is the next number
x+1 +1 is the next number
The sum of these three number is
x + x+1 + (x+1+1) = 438
Combine like terms
3x +3 = 438
Subtract 3 from each side
3x+3-3 = 438-3
3x= 435
Divide by 3
3x/3=435/3
x = 145
x+1 =146
x+1+1 = 147