Q. 71 - Intermediate Algebra

Question

1. Solve the system of equations $\left\{\begin{array}{l}x+y=10\\ x-y=6\end{array}\right.$(a) by graphing (b) by substitution (c) Which method do you prefer? Why?

Step-by-Step Solution

Answer

Solutions of equation $\left\{\begin{array}{l}x+y=10\\ x-y=6\end{array}\right.$

Part (a) Graphically is shown below:

Part (b) Algebraically:

The solution of liner equation is $(8,2)$

Part (c)

Graphical method is more convenient as less step is required to find solution.

Part (a) Step 1. Given information and Table of values

We have been given equation:$\left\{\begin{array}{l}x+y=10\\ x-y=6\end{array}\right.$

To find solution graphically firstly we need to 

 graph the equations, for that we need to create a table of values.

Table of values for: $x+y=10$is shown below:

x	0	2	6	8	10
y	10	4	8	2	0

Table of values for: $x-y=6$ is shown below:

x	0	10	6	2	8
y	-6	4	0	-4	2

Part (a) Step 2. Plotting graph

Plot each coordinates and join the coordinates with a smooth curve in order to obtain graph.

Part (b) Step 1 solving for y

Solve the first equation for$y$.

$x+y =10$

$y =10-x$

Substituting$y=10-x$ in second equation

to solve for $x$

$x-(10-x) =6$

$x=16÷2$

$x=8$

Part (b) Step 2. Solving for y

Substituting $x=8$ into equation $2$ and solve for $y$

$\begin{array}{c}x-y=6\\ 8-y=6\\ -y=6-8\\ -y=-2\\ y=2\end{array}$

Solution of given equation algebraically is $(8,2)$ 

Part (c) Step 1. Finding best method

We can that both the equation can be easily solved using graphical method, So graphical method is more convenient as less step is required to find solution.