Question

How do you solve \[2x+y=12\] and \[3x-y=13\]?

Answer 1

Hint: For the given question we are given to solve the equation \[2x+y=12\] and \[3x-y=13\]. To solve this problem we have to rewrite the first equation in terms of ‘y’ and then we have to substitute it in the second equation to get the values of ‘x’ and ‘y’.

Complete step by step solution:
\[2x+y=12\] and \[3x-y=13\]
Now we have to write both equations as equation(1) and equation (2)
\[2x+y=12............\left( 1 \right)\]
\[3x-y=13............\left( 2 \right)\]
And now we have to take equation(1) and send \[2x\]to right hand side
\[\Rightarrow y=12-2x\]
And we should consider the above equation as equation(3)
\[\Rightarrow y=12-2x............(3)\]
And now we have to substitute y coefficient in equation(2)
\[\Rightarrow 3x-(12-2x)=13\]
And now we have to continue the further equation step by step
\[\Rightarrow 3x-12+2x=13\]
And now we have send the numerical which is present on left hand side had to be send to the right hand side
\[\Rightarrow 3x+2x=13+12\]
And now by adding the both sides which is known as left hand side and right hand side we get a equation
\[\Rightarrow 5x=25\]
Now by calculating the above equation we get the solution of x
\[\Rightarrow x=5\]
And now we have to find the value of y. we all know that the value of x is 5 so by substituting x into the equation(3) we will get the value of y
\[\Rightarrow y=12-2x\]
After substituting \[x=5\]in equation(3) we get
\[\Rightarrow y=12-2(5)\]
\[\Rightarrow y=12-10\]
\[\Rightarrow y=2\]
And now we take \[x=5\]as equation(4) and \[y=2\]as equation(5)
\[\Rightarrow x=5............(4)\]
\[\Rightarrow y=2............(5)\]
Both the above equations are the solutions of the given question

Note: We should be careful while doing substituting method, the common mistake students will do is finding value of x and substituting it in y in the second equation. It will make our problem wrong. So, we should be careful while substituting.