Chapter ISG, Problem 6.4.7P

To determine

To solve the system.

Answer to Problem 6.4.7P

  $x=\frac{1}{3}$ and $y=\frac{-1}{2}$ are the solution

Explanation of Solution

Given information:

  $\begin{array}{l}3x+y=\frac{1}{2}\\ -6x+\frac{1}{2}y=-\frac{9}{4}\end{array}$

Calculation:

Let’s assume the equations 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 3& in equation 2, coefficient of x is -6. To make the coefficients same, lets multiply equation 1 with 2.

  $2\times (3x+y)=\frac{1}{2}\times (2)$

Solving,

  $6x+2y=1$   (3)

Now, add (3) and (2)

  $6x+2y-6x+\frac{1}{2}y=1-\frac{9}{4}$

Solving,

  $2y+\frac{1}{2}y=\frac{4-9}{4}$

So,

  $\frac{5y}{2}=\frac{-5}{4}$

And,

  $y=\frac{-5\times 2}{4\times 5}$

  $y=\frac{-1}{2}$

Put value of y in (1)

  $3x+(\frac{-1}{2})=\frac{1}{2}$

Solving,

  $\begin{array}{l}3x=\frac{1}{2}+\frac{1}{2}\\ 3x=1\end{array}$

Dividing equation by 3,

  $x=\frac{1}{3}$

Hence, $x=\frac{1}{3}$ and $y=\frac{-1}{2}$ are the solution of system.