How do I solve 9p=2q-6 3p-q=12 using substitution?

Question

The problem is
9p=2q-6
3p-q=12

I dont know how to do substitution please help and list steps and details
thank you

Answer 1

Substitution is the method you will most likely use when solving this type of problem.



First, you have to take one of the equations and solve it for one variable in terms of the other. It doesn't matter which one you use, you'll get the same answer. So go with what may be the easiest.



solving for the q in the 2nd equation seems to be the easier approach, so I'll do that:



3p - q = 12

-q = 12 - 3p

q = -12 + 3p



Now we have an expression for q. Now we substitute the value of (-12 + 3p) for q in the other equation, then we can solve for p:



9p = 2q - 6

9p = 2(-12 + 3p) - 6

9p = -24 + 6p - 6

3p = -30

p = -10



Now that we have a value for p, substitute that into either of the two equations and solve for q.



q = -12 + 3p

q = -12 + 3(-10)

q = -12 - 30

q = -42



The answer to the set of equations is:



p = -10

q = -42

Answer 2

Hi C,



Let:



[1] 9p=2q-6.

[2] 3p-q=12.



Rearrange [2] by adding q:



3p = 12 + q.



Then subtract 12:



3p - 12 = q.



Put this version of q into [1]:



9p = 2q - 6 = 2 * (3p - 12) - 6.



Expand the brackets:



9p = 6p - 24 - 6.



Subtract 6p:



3p = - 24 - 6 = - 30.



Divide by three:



p = - 10.



Put this version of p into [2]:



3p - q = 12.



3 * (- 10) - q = 12.



Multiply out:



-30 - q = 12.



Add 30:



-q = 42.



Multiply by -1:



q = - 42.



Solution:



p = - 10.

q = - 42.

Answer 3

3p-q=12

=> q= 3p -12

put p = 3p -12, to get

=> 9p = 2(-12+3p)-6

=> 9p = -24+6p-6

=> 3p=-24-6

=> p=-10

put p = -10 in 1st eqn, to get

=> 3(-10) - q = 12

=> -30-q = 12

= > -q= 42

=> q= - 42

Answer

Answer 4

To do substitution, solve one of your equations for one variable, then "substitute" that into the other equation.



Looking at your two equations, the only variable with no coefficient is the -q in the second one, so solve that for q.



3p - q = 12

-q = -3p + 12

q = 3p - 12



Now you know what q equals, so "substitute" that into the first equation & solve for the other variable



9p = 2q - 6

9p = 2(3p - 12) - 6

9p = 6p - 24 - 6

9p - 6p = -24 - 6

3p = -30

p = -30/3 = -10



q = 3p - 12 = 3*(-10) - 12

q = -42



q = -48



p = -12, q = -48

Answer 5

9p=2q-6 equation (1)

3p-q=12 equ. (2)

then 4rm equ. 1 make p d subject of formular P=2q-6 all over 9.

In equ. 2 subtitute p=2q-6allover9 into equ. 2

dat is 3p-q=12,so put 3(2q-6allova9)-q=12,get q=-42 work t vry wel and get ur p as -10 Goodluck

Answer 6

9p=2q-6

3p-q=12



3p-q+q=12+q

3p-12=q+12-12

3p-12=q

sub 3p-12 for q

9p=2(3p-12)-6

(9p=6p-30)/3

3p=2p-10

now use common sense to find p, if 2p-10=3p then 1p=-10 because 2(-10)-10=3(-10)

-90=2q-6

-84=2q

-42=q

Answers:



p=-10

q=-42

Answer 7

9p=2q-6



3p-q=12

add q to both sides



3p=q+12

subtract 12 from both sides



q=3p-12



substitute 3p-12 for q in 9p=2q-6

9p=2(3p-12)-6

distribute the 2



9p=6p-24-6

9p=6p-30

subtract 6p from both sides

3p=-30

divide by 3



p=-10

Answer 8

given

9p=2q-6

3p-q=12

to solve using substitution

9p=2q-6

9p+6=2q

q=(9p+6)/2

Sub it in 3p-q=12



3p-(9p+6)/2=12

6p-9p-6=24

-3p=30

p=-10

q=(9p+6)/2

q=(-9*10+6)/2

q=-84/2

q=-42



Solution p=-10 q=-42





Hope it helps

Answer 9

You have to solve for one value and then plug it in .



3p-q=12

-q=12-3p

q=-12+3p



9p=2(-12+3p)-6

9p=-24+6p-6

3p=-24-6

p=-10



3(-10)-q=12

-30-q=12

-q=42

q=-42

Answer 10

a million.) 3(4x+a million a million/2y + 2) - 5(2x + a million a million/2y)=0 2(3x - 3y + a million) - 2(2x - 2 a million/2y+4)=0 12x + 4y + 6 - 10x - 7y = 0 2x - 3y + 6 = 0 6x - 6y + 2 - 4x + 5y - 8 = 0 2x - y - 6 = 0 convert one equation to appear like, x= or y= 2x-y-6=0 -y = -2x+6 y = 2x-6 making use of the 2d equation, enter y to clean up for x 2x-3y+6=0 2x - 3(2x-6) + 6=0 2x-6x+18+6=0 -4x+24=0 -4x=-24 x = 6 making use of the unique equation, enter x to clean up for y 2x-y-6=0 2(6)-y-6=0 12-y-6=0 6-y=0 -y=-6 y = 6 x = 6, y = 6 to envision your answer enter the two x and y into between the equations, and it might come out.

Answer 11

solve for q in the second equation, then substitute that in the first equation.



q = 3p-12

9p=2(3p-12)-6

9p=6p-24-6

9p=6p-30

3p=-30

p=-10

then

q=-42..

Answer 12

q = 3p - 12



9p = 6p - 24 - 6

3p = - 30

p = - 10



q = - 30 - 12

q = - 42



p = -10 , q = - 42

Answer 13

i cant work it right now because of my lack of paper but isolate the "p" or "q" and then use simple algebra to continue on with the problem