Question

How do you solve \[2x+y=5\] and \[x+y=4\]?

Answer 1

Hint: For the given question we are given to solve the equation \[2x+y=5\] and \[x+y=4\]. Now we have to rewrite the equation in terms of x and should be equal to y as \[y=5-2x\] and then substitute this in equation (2) to have the results.

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

Note: We can do this problem even by elimination method. For doing that we have to equalize either coefficient of x or y in both sides of the equation and then by doing addition or subtraction we will get the values of x and y.