Question

Solve by elimination method:
$\begin{gathered}
  2x + 5y = 12 \\
  7x + 3y = 13 \\
\end{gathered} $

Answer 1

Hint: In elimination method, we remove one variable to find the value of the other by using both the equations. Then substituting this value in either of the equations, we get the value of the second variable.
Complete step by step answer:
This is a two variables and two equations problem. Our equations are:
1. $2x + 5y = 12$
2. $7x + 3y = 13$
First we will remove $y$ from using both the equations, so that we will be left with $x$. Multiplying (1) by 3 on both sides and (2) by 5 on both sides, we get,
3. $6x + 15y = 36$
4. $35x + 15y = 65$
Subtracting (3) from (4), we cancel $y$ terms because of equal coefficients and we get following:
$\begin{gathered}
   \Rightarrow 29x = 29 \\
   \Rightarrow x = 1 \\
\end{gathered} $
Now, we will substitute this value of $x$ in equation (1), to find the value of $y$.
$\begin{gathered}
   \Rightarrow 2 \times 1 + 5y = 12 \\
   \Rightarrow 5y = 12 - 2 = 10 \\
   \Rightarrow y = 2 \\
\end{gathered} $
Note: We can also reach the same result if we substitute $x$ in the second equation. This solution is also like the intersection point of two lines given by the two equations.