Question

How do you solve \[2x-y=3\] and \[x+2y=24\] using substitution?

Answer 1

Hint: For the given question we are given to solve the equation \[2x-y=3\] and \[x+2y=24\]. For that we have to observe the equation that we could solve the equation by examining the equation. For the given question we have to take any one of the coefficients to find the solution.

Complete step by step solution:
\[2x-y=3\] and \[x+2y=24\]
Now we have to write both equations as equation (1) and equation (2)
\[2x-y=3............(1)\]
\[x+2y=24............(2)\]
And now we have to take equation(1) and send \[2x\] to right hand side
\[\Rightarrow -y=3-2x\]
We can write this equation in another way to make somewhat easier
\[\Rightarrow y=2x-3\]
And we should consider the above equation as equation(3)
\[\Rightarrow y=2x-3............(3)\]
And now we have to substitute y co-efficient in equation(2)
\[\Rightarrow x+2(2x-3)=24\]
And now we have to continue the further equation step by step
\[\Rightarrow x+4x-6=24\]
And now we have send the numerical which is present on left hand side had to be send to the right hand side
\[\Rightarrow x+4x=24+6\]
And now by adding the both sides which is known as left hand side and right hand side we get a equation
\[\Rightarrow 5x=30\]
Now by calculating the above equation we get the solution of x
\[\Rightarrow x=6\]
And now we have to find the value of y. we all know that the value of x is 6 so by substituting x into the equation(3) we will get the value of y
\[\Rightarrow y=2x-3\]
After substituting \[x=6\] in equation(3) we get
\[\Rightarrow y=2(6)-3\]
\[\Rightarrow y=12-3\]
\[\Rightarrow y=9\]
And now we take \[x=6\] as equation(4) and \[y=9\] as equation(5)
\[x=6............(4)\]
\[y=9............(5)\]
Both the above equations are the solutions of the given question

Note: By equation (4) and equation (5), we can see that the value of x and y are 6 and 9 are respectively. So for verification we can check the answers by substituting the values in equation (1). If we get it as LHS=RHS then our answer will be correct.