Chapter ISG, Problem 6.3.1P

a.

To determine

To write first step of elimination.

Answer to Problem 6.3.1P

Explanation of Solution

Given information:

  $\begin{array}{l}0.4x-2y=6\\ 0.8x+2y=0\end{array}$

The first step of elimination is to make the coefficients of both equations equal.

For example, in given equation,

The coefficient of y is same, but if they were not, multiply both sides, of equation whose coefficient is to be equalled.

b.

To determine

To find the solution

Answer to Problem 6.3.1P

Explanation of Solution

Given information:

  $\begin{array}{l}0.4x-2y=6\\ 0.8x+2y=0\end{array}$

Calculation Let Equation 1 be $0.4x-2y=6$

Let Equation 2 be $0.8x+2y=0$

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 0.4 & in equation 2, coefficient of x is 0.8. To make the coefficients same, lets multiply equation 1 with 2.

  $2(0.4x-2y)=2(6)$

This gives-

  $0.8x-4y=12$  (3)

Now, subtracting equation 2 & equation 1’.

  $0.8x-4y-(0.8x+2y)=12-0$

In the next step, x is eliminated-

  $0.8x-0.8x-4y-2y=12$

Hence,

  $-6y=12$

So, $y=-2$

Put value in (3)

  $0.8x-4(-2)=12$

Solving,

  $0.8x+8=12$

So,

  $0.8x=4$

Dividing by 0.8,

  $x=5$

Hence,

  $x=5$ and $y=-2$ is the solution.

c.

To determine

To graph the equation

Explanation of Solution

Given:

  $\begin{array}{l}0.4x-2y=6\\ 0.8x+2y=0\end{array}$

Graph:

The blue line represents: 0. 4x - 2y=6

The black line represents: 0. 8x + 2y =0

  

Interpretation:

The intersection point of the line is (-2, 5) which also the solution of the system

of equation. Hence, the solution is correct.

d.

To determine

To find solution if line changed

Answer to Problem 6.3.1P

Explanation of Solution

Given:

Line changed is $x-5y=15$

Calculation:

Now the lines are:

  $0.4x-2y=6$   (1)

  $x-5y=15$   (2)

So, 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 0.4 & in equation 2, coefficient of x is 1 To make the coefficients same, lets divide equation 1 with 0.4.

  $\frac{0.4x}{0.4}-\frac{2y}{0.4}=\frac{6}{0.4}$

Solving,

  $x-0.5y=1.5$   (3)

Subtracting equations,

  $(x-5y)-(x-0.5y)=15-1.5$

In the next step, x is eliminated.

  $-4.5y=13.5$

Hence,

  $y=-3$

Put in (3)

  $x-0.5(-3)=1.5$

Solving,

  $x=1.5-1.5$

Hence,

x =0