Chapter ISG, Problem 6.4.2P

To determine

Tosolve the system

Answer to Problem 6.4.2P

  $x=13$ and $y=4$ is the solution of given system of equation

Explanation of Solution

Given information:

  $\begin{array}{l}2x-3y=14\\ 6x+y=2\end{array}$

Calculation:

Let’s assume the equation be (1) and (2) respectively

To solve equations by elimination, the given equations are either added or subtracted to get an equation in only one variable.

Let’s eliminate variable x here. To eliminate a variable, the coefficients of the variable must be same in both the equations.

In equation 1, coefficient of x is 2 & in equation 2, coefficient of x is 6. To make the coefficients same, lets multiply equation 1 with 3.

  $3(2x-3y)=3\times 14$

Solving,

  $6x-9y=42$   (3)

Now, subtract the equation(2) and (3),

  $(6x+y)-(6x-9y)=42-2$

Solving,

  $y+9y=40$

So,

  $10y=40$

Dividing equation by 10,

  $y=4$

Put in (1)

  $2x-3(4)=14$

Solving,

  $2x-12=14$

So,

  $2x=26$

Dividing by 2,

  $x=13$

Hence, $x=13$ and $y=4$ is the solution of given system of equation