Here I go
The teacher's system is
-2x + 5y = 10
-3x + 9y = 6
To find the system that equals to the teachers solution, we must solve all three of them. (Yeah good luck)
Let's start solving the teacher's system
We need to solve -2x + 5y = 10 for x
-2x + 5y = 10
-2x = 10 - 5y
Divide both sides by -2
-2x/-2 = (10-5y)/-2
x = 5/2 y - 5
Now we need to substitute 5/2 y -5 for x in -3x +9y = 6
We gonna replace 5/2 y -5 by x
-3x + 9y = 6
-3(5/2 y - 5) + 9y = 6
Simplify both sides (I used a calculator)
3/2 y + 15 = 6
3/2 y = 6 - 15
3/2 y = -9
To find y, we need to divide both sides by 3/2
3/2 y/3/2 = -9/3/2 (I used a calculator)
y = -6
It easier to find x since we already find y
So, let's find x by substitute -6 for y in x=5/2 y - 5
What does that mean? We gonna replace the value of y which is -6 everywhere we find y (I hope it makes sense)
x = 5/2 y - 5
x = 5/2 (-6) - 5 (use a calculator)
x = -20
Therefor,
x = -20 and y = -6
This is the teacher's solution so we gonna solve the others and see what they have :)
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Selina's system
-5x + 14y = 16
-3x + 9y = 12
So, we need to solve -5x + 14y = 16 for x
-5x + 14y = 16
-5x = 16 - 14y
Divide both sides by -5
-5x/-5 = (16 - 14y)/-5
x = 14/5 y + -16/5 (It looks messy here)
To continue, we need to substitute 14/5 y + -16/5 for x in -3x + 9y = 12
-3x + 9y = 12
-3( 14/5 y + -16/5) + 9y = 12
Simplify both sides
3/5 y + 48/5 = 12
3/5 y = 12 - 48/5
3/5 y = 12/ 5
To find y, we just need to divide both sides by 3/5
3/5 y/3/5 = 12/5/3/5 (cancel 5, then divide 12 by 3 = 4)
y = 4
We gonna use the value of y to find x
We gonna do that by substitute 4 for y in x = 14/5 y + -16/5
x = 14/5 y + -16/5
We gonna replace y by 4
x = 14/5 (4) + -16/5 (used a calculator)
x = 8
Therefore,
x = 8 and y = 4
So, Selina system doesn't equal to the teacher's system.
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Goku's system
again, I used the same steps to solve all of them.
x - 3y = -2
-2x + 5y = -7
We need to solve x - 3y = -2 for x
x - 3y = -2
x = -2 + 3y
I prefer to let the unknown value leads, so it will be
x = 3y - 2 (it still the same thing :) )
Substitute 3y - 2 for x in -2x + 5y = -7
-2x + 5y = -7
-2(3y - 2) + 5y = -7
-6y + 4 + 5y = -7
-y + 4 = -7
-y = -7 - 4
-y = -11
We cannot leave the y with a negative sign, so we must divide both sides by -1
-y/-1 = -11/-1
y = 11
To find x, we need to substitute 11 for y in x = 3y - 2
x = 3y - 2
x = (3)(11)-2
x = 33-2
x = 31
Therefore,
x = 31 and y = 11
Goku's answer doesn't equal to the teacher's answer.
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Answer : Neither Goku or Selina
I hope I helped!