Question

Solve the system of equations$x+y=10,x-y=6$

(a) by graphing

(b) by substitution

(c) Which method do you prefer? Why?

Short answer

Part (a) By graph the ordered pair is$(8,2)$

Part (b) By substitution method, the ordered pair is$(8,2)$

Part (c) I would prefer the method of substitution.

Step-by-step solution

Step 1. Given information

The given set of equation are

$$\begin{gathered} x+y=10 \\ x-y=6 \end{gathered}$$

Part (a) Step 1. Graph

Solve the first equation for y and find the slope and y-intercept.

$$\begin{gathered} y=-x+10 \\ m=-1,b=10 \end{gathered}$$

Solve the second equation for y and find the slope and y-intercept.

$$\begin{gathered} y=x-6 \\ m=1,b=-6 \end{gathered}$$

Now, graph the lines on the same rectangular plane,

Form the graph, it is clear that the line intersects at point$(8,2)$. Thus, the solution is$(8,2)$

Part (b) Step 1. Calculation

Solve the first equation for y.

$$\begin{gathered} x+y=10 \\ y=10-x \end{gathered}$$

Substitute the value of y in second equation to find the value of x.

$$\begin{gathered} x-y=6 \\ x-(10-x)=6 \\ 2x=16 \\ x=8 \end{gathered}$$

Find the value of variable y by substituting the value of x.

$$\begin{gathered} y=10-8 \\ y=2 \end{gathered}$$

Thus, the solution is$(8,2)$

Part (c) Step 1. Explanation

I would always prefer the method of substitution because this method is very simple to solve. In graph there is need to plot graph which is not always easy to plot the graph.