Question

Find the value of a and b if \[3a+5b=26\] and \[a+5b=22\] .

Answer 1

Hint: Find the value of a in terms of b from the equation \[a+5b=22\] and then put the value of a that is \[a=22-5b\] in the equation \[3a+5b=26\]. Now, our equation is a linear equation in b and it can be solved further.

Complete step-by-step answer:
According to question, we have
\[3a+5b=26\]……………….(1)
\[a+5b=22\]………………….(2)
We have to find the value of a and b and we also have two equations which are given. For that we have to first find the value of one variable in terms of another variable using equation (2) and then we have to substitute that variable in the equation (1).
Now, we have to find the value of a using equation (2).
\[a+5b=22\]
\[\Rightarrow a=22-5b\]………………(3)
We have got the value of the variable a in terms of b.
Now, using equation(3) and substituting the value of variable a in equation (1), we get
\[\begin{align}
  & 3a+5b=26 \\
 & \Rightarrow 3(22-5b)+5b=26 \\
 & \Rightarrow 66-15b+5b=26 \\
\end{align}\]
Taking the terms of b to the RHS of the above equation, we get
\[\begin{align}
  & \Rightarrow 66-26=15b-5b \\
 & \Rightarrow 40=10b \\
 & \Rightarrow 4=b \\
\end{align}\]
We have \[b=4\] .
Now, putting the value of b in equation (3), we can find the value of a.
\[\begin{align}
  & a=22-5b \\
 & \Rightarrow a=22-20 \\
 & \Rightarrow a=2 \\
\end{align}\]
Hence, the value of a and b are 2 and 4 respectively.

Note: This question can also be solved in another way. According to question, we have two equations, which are
\[3a+5b=26\]……………….(1)
\[a+5b=22\]………………….(2)
Now, we have to find the values of a and b from the given two equations.
Subtracting equation (2) from equation (1), we get
\[\begin{align}
  & 2a=4 \\
 & \Rightarrow a=2 \\
\end{align}\]
Now, putting the value of a in equation (2), we get
\[\begin{align}
  & a+5b=22 \\
 & \Rightarrow 5b=22-a \\
 & \Rightarrow 5b=22-2 \\
 & \Rightarrow 5b=20 \\
 & \Rightarrow b=4 \\
\end{align}\]
Hence, the value of a and b are 2 and 4 respectively.