Solving thru combination: If 6a+6b=30 and 3a+2b=14 what is value of b?

Illvoices

Junior Member
Joined
Jan 13, 2017
Messages
116
If 6a+6b=30 and 3a+2b=14 what is the value of b?

How should I solve this by combination? I tried but I can't get it.
 
If 6a+6b=30 and 3a+2b=14 what is the value of b?

How should I solve this by combination? I tried but I can't get it.
It is just excellent that you tried. Now please show us your work so that we can show you where you went wrong and to also have an idea as to what method you already know.
 
What i did was try 'n use combination. So 6a+6b=30
I isolated a the variable a to get its value. So 6a=30-6b
Then I divided the term by 6 on both sides. So a=5-6\5b
After that I didn't know what to do whether i should of added it to the value of a or kept simplifying it by dividing 6 and 5.
 
What i did was try 'n use combination. So 6a+6b=30
I isolated a the variable a to get its value. So 6a=30-6b
Then I divided the term by 6 on both sides. So a=5-6\5b
After that I didn't know what to do whether i should of added it to the value of a or kept simplifying it by dividing 6 and 5.
I am not sure what you mean by So a=5-6\5b, but whatever you do mean it is wrong (sorry).

The 1st step (actually maybe it is better to call it step 0) is to see if in each equation whether or not there is a common factor to divide by. Now in 6a+6b=30, there clearly is a common factor, so please divide by it and then solve for a.

Also, as practice, please solve for a again in 6a+6b=30 without dividing by the common factor first.
 
What i did was try 'n use combination. So 6a+6b=30
I isolated a the variable a to get its value. So 6a=30-6b
Then I divided the term by 6 on both sides. So a=5-6\5b
After that I didn't know what to do whether i should of added it to the value of a or kept simplifying it by dividing 6 and 5.
Okay; that's not "combination" (also known as "elimination" or "addition"); that's substitution. Instead, try combining the two equations:

. . . . .6a + 6b = 30
. . . . .3a + 2b = 14

If the second equation is multiplied by -3, then the b-terms would cancel out when the equations are combined by adding down. But if the second equation were multiplied by -2, then the a-terms would cancel out, plus I'd be dealing with smaller numbers. So let's multiply the second line by -2:

. . . . .+6a + 6b = +30
. . . . .-6a - 4b = -28

Add down, etc, etc. ;)
 
Okay; that's not "combination" (also known as "elimination" or "addition"); that's substitution. Instead, try combining the two equations:

. . . . .6a + 6b = 30
. . . . .3a + 2b = 14

If the second equation is multiplied by -3, then the b-terms would cancel out when the equations are combined by adding down. But if the second equation were multiplied by -2, then the a-terms would cancel out, plus I'd be dealing with smaller numbers. So let's multiply the second line by -2:

. . . . .+6a + 6b = +30
. . . . .-6a - 4b = -28

Add down, etc, etc. ;)
When I multiplied by negative two and eliminated the a value I got 2b=2.
I believe that further down you divide by two and and get b equals 1.
Then plug in for b and get the correct answer.
 
What i did was try 'n use combination. So 6a+6b=30
I isolated a the variable a to get its value. So 6a=30-6b
Then I divided the term by 6 on both sides. So a=5-6\5b
I think you accidently used "5" in one of those divisions: a= 30/6- (6b)/6= 5- b.

After that I didn't know what to do whether i should of added it to the value of a or kept simplifying it by dividing 6 and 5.
Putting that back into the second equation, 3a+ 2b= 3(5- b)+ 2b= 15- 3b+ 2b= 15- b= 14 so b= 15- 14= 1.
 
Divide 1st equation by 6: a + b = 5
So a = 5 - b
Substitute in 2nd equation...
Except that the instructions clearly said to use "combination", not substitution. ;)
 
When I multiplied by negative two and eliminated the a value I got 2b=2.
I believe that further down you divide by two and and get b equals 1.
Then plug in for b and get the correct answer.
No, no! The problem asked you to solve for b. Since you know b=1 you are done. There is no need to solve for a.
 
Top