Chapter ISG, Problem 6.9STP

To determine

To solve the system.

Answer to Problem 6.9STP

  $x=-3$ and $y=-7$ are the solutions

Explanation of Solution

Given information:

  $\begin{array}{l}3x-2y=5\\ 4x-3y=9\end{array}$

Calculation:

Let’s assume equations be (1) and (2)

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 3 & in equation 2, coefficient of x is 4. To make the coefficients same, lets multiply equation 1 with 4, and equation 2 by 3.

  $3(4x-3y)=9\times 3$ and $4\times (3x-2y)=5\times 4$

Solving,

  $12x-8y=20$   (3) and

  $12x-9y=27$  (4)

Now, subtract equation (3) and (4)

  $12x-9y-12x+8y=27-20$

So,

  $-y=7$

Changing signs,

  $y=-7$

Now, put value of y in equation (1)

  $3x-2(-7)=5$

Solving equation,

  $3x+14=5$

Now,

  $3x=-9$

Dividing equation by 3,

  $x=-3$

Hence, $x=-3$ and $y=-7$ are the solutions of the system