Question

How do you solve the system $2x + 3y = 12$ and $4x - 3y = 6$?

Answer 1

Hint: The given equation is the linear system of equations in two variables. To solve this equation we will use the elimination method. We will eliminate one variable and find the value of another variable and then put the value in any one of the equations to get the value of another (eliminated) variable.

Complete step by step answer:
We have two equations
$
  2x + 3y = 12\, \ldots \ldots (1) \\
  4x - 3y = 6\,\, \ldots \ldots (2) \\
 $
We can eliminate $y$ terms as they are equal and their signs are opposite.
Now, On adding the equation $(1)$ and $(2)$. We get,
$ \Rightarrow 6x = 18$
$ \Rightarrow x = 3$
Here, we get the value of $x$ i.e., $x = 3$
Now, put the value of $x$ in equation $(1)$. We get,
$ \Rightarrow 2(3) + 3y = 12$
$ \Rightarrow 6 + 3y = 12$
Shifting $6$ to the right side of the equation. We get,
$ \Rightarrow 3y = 12 - 6$
$ \Rightarrow 3y = 6$
$ \Rightarrow y = 2$
Therefore, the solution to the given linear equation is $x = 3$ and $y = 2$.

Note: For solving the linear system of equations in two variables by elimination we can only eliminate the variable if the coefficient of variable is same in both the equation and their signs are opposite, if not, first equate them by multiplying the equation with some constant term.
 There are various methods to solve linear systems of equations in two variables such as elimination method, substitution method and cross-multiplication method.