Question

How do you solve \[x-5y=6\] and \[2x+3y=12\] using substitution?

Answer 1

Hint: In this problem, we have to solve and find the values of a and b form the given two equations using substitution. We can first take the first equation and find the value of x in terms of variable y. we can then substitute the x value in another equation so that the equation will have only the variable y, we can solve and find the answer for it, we can then substitute the value of y in any of the equations to get the value of x.

Complete step-by-step solution:
We know that the given equations to be solved is,
\[x-5y=6\]……. (1)
\[2x+3y=12\]……. (2)
We can now take the first equation and write it as,
\[\Rightarrow x=6+5y\]
We can now substitute the above value of x in (2), we get
\[\Rightarrow 2\left( 6+5y \right)+3y=12\]
We can now simplify the above steps, we get
\[\begin{align}
  & \Rightarrow 12+10y+3y=12 \\
 & \Rightarrow 13y=0 \\
 & \Rightarrow y=0 \\
\end{align}\]
The value of y is 0.
We can now substitute y value in (1), we get
\[\begin{align}
  & \Rightarrow x-0=6 \\
 & \Rightarrow x=6 \\
\end{align}\]
Therefore, the value of x = 6 and y = 0.

Note: We should know that we can substitute the first resulted value in any of the given equations to get the other value. 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 x = 6, y = 0 in equation (2), we get
\[\begin{align}
  & \Rightarrow 2\left( 6 \right)+5\left( 0 \right)=12 \\
 & \Rightarrow 12+0=12 \\
\end{align}\]
Therefore, the values are correct.