Question

Solve the following system of equations by elimination method:
\[2x + 5y = 1\]
\[2x + 3y = 3\]

Answer 1

Hint: Here we are asked to solve the given equations for the value of $x$ and $y$ by using the elimination method. Since they have mentioned that we have to use the elimination method we are not supposed to use any other method. In elimination method, any one of the unknown variables will be eliminated and solved for the other variable. Then the value of that variable is substituted in any one of the equations given to find the value of the other unknown variable.

Complete answer:
We are given the equations \[2x + 5y = 1\], \[2x + 3y = 3\] we aim to solve these equations by the elimination method to find the value of $x$ and $y$ .
As we see that the coefficients of the \[x\] term in both the equations are same we can easily perform subtraction to eliminate the variable and proceed further,
\[2x + 5y = 1\]---------\[(1)\]
\[2x + 3y = 3\]---------\[(2)\]
Subtracting \[(2)\] from \[(1)\] and simplifying it we get,
\[2x + 5y - 1 - (2x + 3y - 3) = 0\]
\[ \Rightarrow 2x + 5y - 1 - 2x - 3y + 3 = 0\]
\[ \Rightarrow 2y + 2 = 0\]
\[ \Rightarrow 2y = - 2\]
\[ \Rightarrow y = - 1\]
Now substituting \[y = - 1\] in equation \[(1)\] and simplifying it we get,
\[2x + 5y = 1\]
\[ \Rightarrow 2x + 5.( - 1) = 1\]
\[ \Rightarrow 2x = 1 + 5\]
\[ \Rightarrow 2x = 6\]
\[ \Rightarrow x = 3\]
Therefore, the solution for the equations is \[(3, - 1)\]

Note:
In the above problem, we have solved the problem by the elimination method. In the elimination method, while eliminating any one of the unknown variables we will modify the given equation only by using multiplication or division; we are not supposed to use addition or subtraction for that modification. Students must pay attention in small steps like integer addition and subtraction because there may be a chance of doing mistakes since we have positive and negative signs in integers which decides the operation to be done in that step.