Question

How do you solve \[2x-y=2\] and \[2x+3y=22\]?

Answer 1

Hint: For the given question we are given to solve the equation \[2x-y=2\] and \[2x+3y=22\]. We will obtain y in terms of x from the first equation as \[y=2x-2\]. Then, we will substitute it in the second equation and obtain the value of x. We can then easily find the value of y by substituting x in \[y=2x-2\]. Hence, we will have our results.

Complete step by step solution:
\[2x-y=2\] and \[2x+3y=22\]
Now we have to write both equations as equation (1) and equation (2)
\[2x-y=2............(1)\]
\[2x+3y=22............(2)\]
And now we have to take equation (1) and send \[2x\] to right hand side
\[\Rightarrow -y=2-2x\]
We can write this equation in another way to make somewhat easier
\[\Rightarrow y=2x-2\]
And we should consider the above equation as equation (3)
\[\Rightarrow y=2x-2............(3)\]
And now we have to substitute y coefficient in equation (2)
\[\Rightarrow 2x+3(2x-2)=22\]
And now we have to continue the further equation step by step
\[\Rightarrow 2x+6x-6=22\]
And now we have sent the numerical which is present on left hand side had to be send to the right-hand side
\[\Rightarrow 2x+6x=22+6\]
And now by adding the both sides which is known as left hand side and right-hand side we get an equation
\[\Rightarrow 8x=28\]
Now by calculating the above equation we get the solution of x
\[\Rightarrow x=3.5\]
And now we have to find the value of y. we all know that the value of \[x=3.5\] so by substituting x into the equation (3) we will get the value of y
\[\Rightarrow y=2x-2\]
After substituting \[x=3.5\] in equation (3) we get
\[\Rightarrow y=2(3.5)-2\]
\[\Rightarrow y=7-2\]
\[\Rightarrow y=5\]
And now we take \[x=3.5\] as equation (4) and \[y=5\] as equation(5)
\[\Rightarrow x=3.5............(4)\]
\[\Rightarrow y=5............(5)\]
Both the above equations are the solutions of the given question.

Note: We can do this problem even by substituting the both equations given but the solution we did is the best and the elimination method to solve the given question which is much easier for the students to solve.