Chapter 13.3, Problem 1PSA

(a)

To determine

To find: The point of intersection of the graphs of each system.

Answer to Problem 1PSA

The point of intersection is $\left(6,4\right)$ .

Explanation of Solution

Given:

The given system of equation is:

  $\begin{array}{c}x+y=10\left(1\right)\\ x-y=2\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}x+y+\left(x-y\right)=10+2\left[\text{adding both the equation}\right]\\ 2x=12\\ x=6\\ 6+y=10\left[\text{substitute}x=6\text{in equation}\left(1\right)\right]\end{array}$

Further simplified as:

  $y=4$ .

Therefore the point of intersection is $\left(6,4\right)$ .

(b)

To determine

To find: The point of intersection of the graphs of each system.

Answer to Problem 1PSA

The point of intersection is $\left(2,5\right)$ .

Explanation of Solution

Given:

The given system of equation is:

  $\begin{array}{c}y=5\left(1\right)\\ x+y=7\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}x+5=7\left[\text{substitute}y=5\text{in equation}\left(2\right)\right]\\ x=2\end{array}$

Therefore the point of intersection is $\left(2,5\right)$ .

(c)

To determine

To find: The point of intersection of the graphs of each system.

Answer to Problem 1PSA

The point of intersection is $\left(-3,-7\right)$ .

Explanation of Solution

Given:

The given system of equation is:

  $\begin{array}{c}y=2x-1\left(1\right)\\ y=4x+5\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}2x-1=4x+5\left[\text{putting}\left(1\right)=\left(2\right)\right]\\ 2x=-6\\ x=-3\\ y=2\left(-3\right)-1\left[\text{substitute}x=-3\text{in equation}\left(1\right)\right]\end{array}$

Further simplified as:

  $y=-7$ .

Therefore the point of intersection is $\left(-3,-7\right)$ .

(d)

To determine

To find: The point of intersection of the graphs of each system.

Answer to Problem 1PSA

The point of intersection is $\left(3,2\right)$ .

Explanation of Solution

Given:

The given system of equation is:

  $\begin{array}{c}x+2y=7\left(1\right)\\ 4x-y=10\left(2\right)\end{array}$

Calculation:

The point of intersection is calculated as:

  $\begin{array}{c}4x+8y-\left(4x-y\right)=28-10\left[\text{multiplying equation}\left(1\right)\text{by 4 and then subtract equation}\left(2\right)\right]\\ 9x=18\\ x=2\\ 4x-2=10\left[\text{substitute}y=2\text{in equation}\left(2\right)\right]\end{array}$

Further simplified as:

  $x=3$ .

Therefore the point of intersection is $\left(3,2\right)$ .