Question

How do you solve \[3a-b=11\] and \[2a+3b=0\] using substitution?

Answer 1

Hint: In this problem, we have to solve and find the values of a and b from the equations given using substitution. We can multiply the number 3 on both sides in the first equation to get similar terms to be cancelled in the elimination. We can then substitute the resulting value a or b, in any of the given equations, to get the other value.

Complete step by step answer:
We know that the given equations to be solved is,
\[3a-b=11\]……. (1)
\[2a+3b=0\]……. (2)
We can now multiply the number 3 on both sides of the equation (1), we get
\[\Rightarrow 9a-3b=33\]…… (3)
Now we can add the equation (2) and (3), so that we can get similar terms to be cancelled in the elimination and we will get one of the values of m or n.
\[\Rightarrow 2a+3b+9a-3b-33=0\]
Now we can simplify the above step, we get
\[\begin{align}
  & \Rightarrow 2a+9a-33=0 \\
 & \Rightarrow 11a-33=0 \\
 & \Rightarrow a=3 \\
\end{align}\]
Now we can substitute the above value in the equation (2) and simplify, we get
\[\begin{align}
  & \Rightarrow 3\left( 3 \right)-b=11 \\
 & \Rightarrow 9-b=11 \\
 & \Rightarrow b=-2 \\
\end{align}\]
Therefore, the value of a = 3 and the value of b = -2.

Note:
Students make mistakes while multiplying the correct numbers to get the same terms to get cancelled in the elimination. We should concentrate on the part of substitution, by substituting the value in any of the given equations. We can also apply the resulting values in any of the equations, to check whether the values found are correct.
We can substitute the value a = 3, b = -2 in equation (1), we get
\[\begin{align}
  & \Rightarrow 3\left( 3 \right)-\left( -2 \right)=11 \\
 & \Rightarrow 9+2=11 \\
\end{align}\]
Therefore, the values are correct.