Question

Using the method of elimination, find the value of x and y from the equations \[2x-3y=1\] and \[x+2y=-3\] .

Answer 1

Hint: Multiply by 2 in the equation \[x+2y=-3\] and subtract it from the equation \[2x-3y=1\].
Now, solve it and find the value of y. Then put the value of y any one of the given two equations and find the value of x.

Complete step-by-step answer:
According to the question, we have two equations that are given.
\[2x-3y=1\]……………(1)
\[x+2y=-3\]………………(2)
In elimination method, we have to remove one variable term after doing some addition or subtraction of the given two equations.
Let us try to eliminate terms of x. We have 2x terms in equation (1) but we have only x in equation (2). We have to make 2x terms in equation (2).
So, multiplying by 2 in equation (2), we get
\[2x+4y=-6\]………………(3)
Now, we have the term 2x in equation (3) and equation (1) as well.
Subtracting equation (3) from equation (1), we get
\[\begin{align}
  & 2x-3y-2x-4y=1-(-6) \\
 & \Rightarrow -7y=7 \\
 & \Rightarrow y=-1 \\
\end{align}\]
Now, we have got the value of y.
Putting the value of y in equation (1), we get
\[\begin{align}
  & 2x-3(-1)=1 \\
 & \Rightarrow 2x+3=1 \\
 & \Rightarrow 2x=1-3 \\
 & \Rightarrow 2x=-2 \\
 & \Rightarrow x=-1 \\
\end{align}\]
We also got the value of x.
Hence, the value of x and y is equal to -1.

Note: We can also solve this equation by substituting the value of x. We can find the value of x in terms of y using equation (1) and then put the value of x in equation (2). Our equation (2) will become a linear equation in y and hence, we can find the value of y. But this approach is wrong because we are using substitution methods and we are asked to solve using elimination methods only.