Question

How do you solve the system \[6x-y=-145\] and \[x=4-2y\] ?

Answer 1

Hint: Assume the given equations as equation (1) and (2) respectively. Now, consider equation (2) where the value of x is given in terms of y. Substitute this value of x in equation (1) and solve for the value of y. Once the value of y is found, substitute it in equation (2) to find the value of x.

Complete step-by-step solution:
Here, we have been provided with the two equations: \[6x-y=-145\] and \[x=4-2y\] and we are asked to solve this system, that means we have to find the values of the variables x and y.
Now, let us assume the two given equations as equation (1) and (2) respectively, so we have,
\[\Rightarrow 6x-y=-145\] - (1)
\[\Rightarrow x=4-2y\] - (2)
Let us apply the substitution method to solve the above question. Here, we will substitute the value of the variable x, which is given in equation (2), in equation and solve for the value of y.
Once the value of y is found we will substitute this obtained value in equation (2) to get the value of x.
So, now substituting the value of x given in terms of y from equation (2) in equation (1), we get,
\[\begin{align}
  & \Rightarrow 6\left( 4-2y \right)-y=-145 \\
 & \Rightarrow 24-12y-y=-145 \\
 & \Rightarrow 24-13y=-145 \\
 & \Rightarrow 13y=24+145 \\
 & \Rightarrow 13y=169 \\
\end{align}\]
Dividing both the sides with 13 and simplifying, we get,
\[\Rightarrow y=13\]
Now, substituting the above obtained value of y in equation (2), we get,
\[\begin{align}
  & \Rightarrow x=4-2\left( 13 \right) \\
 & \Rightarrow x=4-26 \\
 & \Rightarrow x=-22 \\
\end{align}\]
Hence, the solution of the given system of equations is given as: - \[\left( x,y \right)=\left( -22,13 \right)\].

Note: One may note that we can also substitute the value of y from equation (1) in equation (2) and then find the value of x first. This will also give the same answer. You may check the answer by substituting the values of x and y obtained, in the given equations. If L.H.S. and R.H.S. turns out to be the same for both the cases then our answer is correct. Remember that we can also solve the system by the elimination method or by the cross – multiplication method. Here, we have applied the substitution method because the value of x in terms of y was already provided to us in equation (2).