2A + B = 310 A + 2B = 240 What are A and B?

Question

I remember doing these problems in algebra class, but it's been awhile, and I'm trying to remember how to do it. Can anybody explain?

Answer 1

2A + B = 310
+
-2(A + 2B = 240)
------------------------------
-3B = -170 ----> B = 170/3
2A + 170/3 = 310
2A = 760/3 ---> A = 380/3

Answer 2

This is a classic Linear Combination problem. Set up the equations on top of each other so the variables are parallel to each other, like so:

2A+B=310
A+2B=240

In the combination method, your trying to multiply one equation so that with the end product, one of the variables will be cancelled out. this equation is particularly easy to because the coefficients are 1 and 2. Lets try to cancel out variable A. Since the first equation has 2A+B=310, well need to multply our second equation by -2 so that at the end, the 2A and -2A will cancel out, lets see how it looks:

2A+B=310
-2(A+2B=240)

= 2A+B=310
-2A-4B=-480
____________

-3B=-170

B=170/3


Although normally after you find an answer to one variable, you plug it back into one of the original equations to slove for the last variable. Because this answer isnt a whole number and repeats, it wouldnt be wise to plug it in and try to solve it. Simply do the exact same steps to slove for letter A instead of letter B this time.

Your final answers should be:

B=170/3
A= 380/3

Answer 3

Elimination by addition Method

2A + B = 310- - - - - -Equation 1
A + 2B = 240- - - - - Equation 2
- - - - - - - - - - -

Multiply equation 1 by - 2

2A + B = 310

- 2(2A) +(- 2)(B) = - 2(310)

- 4A + (- 2B) = - 620

- 4A - 2B = - 620

- - - - - - - - - - - - - -

Elimination of B

- 4A - 2B = - 620
A + 2B = 240
- - - - - - - - - - - -
- 3A = - 380
- 3A / - 3 = - 380 / - 3

A = 380/3

Insert the A value into equation 1
- - - - - - - - - - - -

2A + B = 310

2(380/3) + B = 310

760/3 + B = 310

760/3 +B - 760/3 = 310 - 760/3

B = 930/3 - 760/3

B = 170/3

Insert the B value into equation 1
- - - - - - - - - - - - -

Check Equation 1

2A + B = 310

2(380/3) + 170/3 = 310

760/3 + 170/3 = 310

930/3 = 310

310/310

- - - - - - - - - - -

Check equation 2

A + 2B = 240

380/3 + 2(170/3) = 240

380/3 + 340/3 = 240

720/3 = 240

240 = 240

- - - - - - - - - - -

Both equations balance

A = 380/3

B = 170/3

- - - - - - - - -s-

Answer 4

2A + B = 310
A + 2B = 240

First multiply the second equation by 2
2A + 4B = 480

Now subtract the first from the second equation

2A + 4B = 480
2A + B = 310

Then

3B = 170
B ≈ 56.6667

Substute B into the first equation and solve for A

2A + 56.6667 = 310
A ≈ 126.6667
.

Answer 5

Just solve the twq equations
Lik 2A + B =310

By making the second equation as
2A +4B=480

Now subtract
We get 3B=170
So B=170/3

Putting this value in any of the equations we get
A=380/3

Answer 6

You solve it simultaneously...
1) 2A+B=240
2) 310A+2B=240

Take 1) and make B the subject, so...
B=240-2A

Sub B into 2) , so...
310A + 2(240-2A)= 240

Solve it, then sub A into B=240-2A

Hope itZ ryt... :P :P :P

Answer 7

2A + B = 310
- 2A - 4B = - 480----ADD
-3B = - 170
3B = 170
B = 170 / 3
2A + 170 / 3 = 310
2A = 930 / 3 - 170 / 3
2A = 760 / 3
A = 760 / 6
B = 170 / 3

Answer 8

2A + B = 310 A + 2B = 240
B = 310-2A
A + 2(310-2A) = 240
A + 620-4A= 240
620-3A= 240
380=3A
A=380/3
B =170/3

Answer 9

2A+B=310
A+2B=240
add; 3A+3B=550
A+B=550/3
A=310-550/3=380/3
B=240-550/3=170/3 answer

Answer 10

i dont get how people have problems doing this stuff... its been a while since i did algebra or geometry but i am doing algebra 2 this coming semester or the one after... uhhh what the guy said above me