Question

Solve the following systems of equations:
$
  \dfrac{x}{3} + \dfrac{y}{4} = 11 \\
  \dfrac{{5x}}{6} - \dfrac{y}{3} = - 7 \\
$

Answer 1

Hint: We will use the method of elimination by equating the coefficients in order to solve this question. After doing so, we will also use subtraction like in the solution below to find out the value of x and y.

Complete step-by-step answer:
According to the question we have to equations i.e. $\dfrac{x}{3} + \dfrac{y}{4} = 11,\dfrac{{5x}}{6} - \dfrac{y}{3} = - 7$
Hence, the equation can be rewritten as :
Equation $\left( 1 \right):4x + 3y = 132$
Equation$\left( 2 \right):5x - 2y = - 42$
Now to make the coefficient equal of any variable of the two equation multiply equation $\left( 1 \right)$by $2$ and equation $\left( 2 \right)$ by $3$, we get
Equation $\left( 1 \right)\; \times \;2:8x + 6y = 264$
Equation $\left( 2 \right)\; \times \;3\;:15x - 6y = - 126$
Add two equations;
$
   \Rightarrow 23x = 138 \\
   \Rightarrow x = 6 \\
$
Substitute the value of $x$ in equation $\left( 1 \right)$, we get;
$ \Rightarrow 3y = 108$
$ \Rightarrow y = 36$

Note: In such types of questions there are four ways of solving the system of linear equations in two variables i.e Graphical Method , Elimination Method , Substitution Method and By Cross – Multiplication Method.