Question

If 3a-2b= 8 and a+3b=7 what is the value of 4a+b?

Answer 1

Step 1: Find the value of one variable in terms of the other.


`a+3b=7\\a=7-3b`

Step 2: Substitute the value you just found for this variable in the other equation.


`3a-2b=8\\3(7-3b)-2b=8\\21-9b-2b=8\\21-11b=8\\21=8+11b\\13=11b\\(13)/(11)=b\\ b=1(2)/(11)`

Step 3: Use your new value for the second variable to find the first.


`a+3b=7\\a+3(1(2)/(11))=7\\a+3(6)/(11)=7\\\\a=3(5)/(11)`

Now that we know the values for a and b we can find the value of 4a+b.


`4a+b\\4(3(5)/(11))+1(2)/(11)\\12+(20)/(11)+1(2)/(11)\\\\12+1(9)/(11)+1(2)/(11)\\\\\boxed{15}`