Question

Solve the following equations by using elimination method.
\[3x+4y=10\ \ \ \ ...(a)\ and\ 2x-2y=2\ \ \ \ ...(b)\]
A. x=2, y=1
B. x=-1, y=-2
C. x=1, y=0
D. x=-2, y=3

Answer 1

Hint: In elimination method, we first try to make the coefficient of any one variable of the two as equal and then subtract or add the new equations accordingly.Then, we will get the equation which will have only one variable.Then we can solve the equation to get the value of that variable which is left and after getting the value of any one variable, we can plug in that value in any of the equations and then get the value of the other variable as well.

Complete Step-by-step answer:
As mentioned in the question, we will first multiply the second equation that is equation (b) by 2.
The equation that we will thus get is
\[4x-4y=4\ \ \ \ \ ...(c)\]
Now, on adding equation (a) and equation (c), we get
\[\begin{align}
  & \ \ \ \ 3x+4y=10 \\
 & \dfrac{+(4x-4y=4)}{7x=14} \\
 & x=2 \\
\end{align}\]
Now, as we know that x=2, then by putting the value of x in equation (a), we get
\[\begin{align}
  & 3x+4y=10 \\
 & 3\times 2+4y=10 \\
 & 4y=10-6 \\
 & y=\dfrac{4}{4} \\
 & y=1 \\
\end{align}\]
Hence,
Value of x=2 and y=1.

Note: For questions in which there are more than 2 variables, in order to know whether the equations are solvable or whether we will be able to get the values of the variables by just counting the number of variables and number of the equations. If the number of equations and the number of variables involved in the question is equal then we can surely say that every variable will be having a unique value. If these numbers are not equal, then we do not comment on that.
There are two other methods of solving a 2 variable system of equations:-
Substitution method
Cross multiplication method