Chapter 6.2, Problem 37PFA

a.

To determine

To find: System of equations to represent this situation .

Answer to Problem 37PFA

  $\begin{array}{l}2x-4y=0\\ x=y+5\end{array}$

Explanation of Solution

Given information:

Sum of two numbers = 3 times of difference of two number

Greater number = 5 + lesser number

Let $x$ be the greater number

Let $y$ be the lesser number

  $\begin{array}{l}\Rightarrow x+y=3\left(x-y\right)\\ \Rightarrow x+y=3x-3y\\ \Rightarrow 3x-x-3y-y=0\\ \Rightarrow 2x-4y=0\end{array}$

  $\Rightarrow 2x-4y=0$ -------- (1)

  $x=y+5$ -------(2)

b.

To determine

To find: Values of lesser and greater numbers .

Answer to Problem 37PFA

Greater value = $x=10$

Lesser value = $y=5$

Explanation of Solution

Given information:

Sum of two numbers = 3 times of difference of two number

Greater number = 5 + lesser number

  $\Rightarrow 2x-4y=0$ -------- (1)

  $x=y+5$ -------(2)

Substitute the value of $x$ from equation-(2) in equation-(1)

We get

  $\begin{array}{l}2x-4y=0\\ \Rightarrow 2\left(y+5\right)-4y=0\\ \Rightarrow 2y+2\left(5\right)-4y=0\\ \Rightarrow 2y+10-4y=0\\ \Rightarrow 4y-2y=10\\ \Rightarrow 2y=10\\ \Rightarrow y=\frac{10}{2}\\ \Rightarrow y=5\end{array}$

Substitute value of $y$ in equation-(2)

We get

  $\begin{array}{l}x=y+5\\ \Rightarrow x=5+5\\ \Rightarrow x=10\end{array}$

Therefore, values of x and y are

Greater number = $x=10$

Lesser number = $y=5$ .

c.

To determine

To find: Could you have substituted for x or y to solve the system of equations ..

Answer to Problem 37PFA

YES

Explanation of Solution

Given information:

Sum of two numbers = 3 times of difference of two number

Greater number = 5 + lesser number

  $\Rightarrow 2x-4y=0$ -------- (1)

  $x=y+5$ -------(2)

Substitute the value of $x$ from equation-(2) in equation-(1)

We get

  $\begin{array}{l}2x-4y=0\\ \Rightarrow 2\left(y+5\right)-4y=0\\ \Rightarrow 2y+2\left(5\right)-4y=0\\ \Rightarrow 2y+10-4y=0\\ \Rightarrow 4y-2y=10\\ \Rightarrow 2y=10\\ \Rightarrow y=\frac{10}{2}\\ \Rightarrow y=5\end{array}$

Substitute value of $y$ in equation-(2)

We get

  $\begin{array}{l}x=y+5\\ \Rightarrow x=5+5\\ \Rightarrow x=10\end{array}$

Therefore, values of x and y are

Greater number = $x=10$

Lesser number = $y=5$ .

YES, we have substituted x or y to solve the system of equations.