Question

Solve the following equation:
\[
  x + 3y = 6 \\
  2x - 3y = 12 \\
 \]

Answer 1

Hint:
To solve these questions, we have to equate any one of the coefficients of each equation and then either add these equations or subtract, through which we get the value of one variable, which we put in the equation to get the value of another variable.
Linear equations are the equations having two different variables and the coefficients of these variables should be non-zero. The form of linear equation is $ax + by = c$, here $a, b$ are the coefficients of variables and $c$ is the constant.
A solution of a linear equation in two variables $ax + by = c$ is a specific point in graph, such that when we want to solve a single linear equation on the graph then the $x$-coordinate of the point is multiplied by $a$, and the $y$-coordinate of the point is multiplied by $b$, and those two numbers are added together, the answer equals $c$. Solution of two linear equations in two variables, we simply want those points that are solutions for both the equations.

Complete step by step solution:
We have two equations
\[
  x + 3y = 6......(1) \\
  2x - 3y = 12......(2) \\
 \]
We will add these two equations with each other
$x + 3y + 2x - 3y = 6 + 12$
$ + 3y$ and $ - 3y$ will be cancel out and $x$ and $2x$ will add up
$\Rightarrow 3x = 18$
$\Rightarrow x = 6$
Here, we get the value of $x$
Now, we will put value of $x$ in equation $(1)$
$6 + 3y = 6$
$ + 6$ both side of equation will be cancel out
$3y = 0$
$\Rightarrow y = 0$

Hence, we get x=6 and y=0 as our required answer.

Note:
We should remember that the coefficient of any one variable of the first equation should be equal to the coefficient of another equation before performing addition or subtraction, otherwise equations get complex to solve.