Solve the system of equations 3y + 2z = 12 and y – z = 9

Answers

The two equations given are:
3y + 2z = 12
y - z = 9
Now let us take the second equation first and find the value of y in relation to z
y = 9 + z
Now we will put the value of y found from the second equation in the first equation.
3y + 2z = 12
3(9 + z) + 2z = 12
27 + 3z + 2z = 12
5z = 12 - 27
5z = -15
z = -(15/5)
   = -3
Now again we will put the value of z in the second equation for finding the value of y
y = 9 + z
  =  9 - 3
  = 6
So we find the value of "y" is 6 and that of "z" is -3
If you would like to solve the system of equations 3y + 2z = 12 and y - z = 9, you can do this using the following steps:

3y + 2z = 12
y - z = 9 ... y = 9 + z

3y + 2z = 12
3 * (9 + z) + 2z = 12
27 + 3z + 2z = 12
5z = 12 - 27
5z = -15
z = -15/5
z = -3

y = 9 + z = 9 - 3 = 6

The correct result would be c. y = 6, z = –3.
3y + 2z = 12
Now you just try every answer until you get the right one.
A) y=6 z=-3
3×6 + 2×(-3) =18 -6=12
This is CORRECT
B) y=24 z=15
3×24 + 2×15= 72 + 30 =102
This is INCORRECT
C) y=6 z=15
3×6 + 2×15=18+30=48
This is INCORRECT
D)y=-6 z=15
3×(-6) + 2×15 = -18 + 30 = 12
This is CORRECT
So the correct answers are A and D
Mulitply second equation by 2 and add to first

3y+2z=12
2y-2z=18 +
5y+0z=30

5y=30
divide 5
y=6

sub back
y-z=9
6-z=9
minus 6
-z=3
times -1
z=--3

x=-3
y=6


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