SOLUTION: Can you please show me how to work this problem out? 2a+b=14 3a+b+4 (this is one problem.)

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Question 7668: Can you please show me how to work this problem out?
2a+b=14
3a+b+4
(this is one problem.)
Found 2 solutions by bonster, glabow:
Answer by bonster(299) About Me  (Show Source):
You can put this solution on YOUR website!
2a+b=14
3a+b+4

Multiply one set with -1 to cancel out b:
-(2a+b=14)
3a+b+4

-2a-b=-14
3a+b+4

add the two verticaly
a=-10



To find b, multiply the first set by 3 and the second by -2:
2a+b=14
3a+b+4

3(2a+b=14)
-2(3a+b=4)

6a+3b=42
-6a-2b=-8
b=34



a=-10
b=34

Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume you meant
2a+b=14
3a+b=4
Solving by substitution means finding b in terms of a in one equation and using that value of b in the second equation.
b = 14 - 2a [subtracting 2a from both sides]
So the second equation is
3a + (14 - 2a) = 4 [replacing b with its value 14 - 2a]
a + 14 = 4 [simplifying 3a-2a]
a = -10 [subtracting 14 from both sides]
Now put the value of a back into the first equation.
2(-10) + b = 14 [substituting the known value of a]
-20 + b = 14 [multiplying]
b = 34 [adding 20 to both sides]
Checking:
2(-10) + 34 = 14
3(-10) + 34 = 4