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.

$3a-2b=8\\3(7-3b)-2b=8\\21-9b-2b=8\\21-11b=8\\21=8+11b\\13=11b\\\frac{13}{11}=b\\ b=1\frac{2}{11}$

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

$a+3b=7\\a+3(1\frac{2}{11})=7\\a+3\frac{6}{11}=7\\\\a=3\frac{5}{11}$

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

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