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

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

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

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

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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