Question

Solve the system graphically Y=7x-3Y=x+3

Answer 1

We will solve as follows:

We graph each line as follows:

*First, we calculate the x & y-intercept points of each line, those are found by replacing y= 0 & x = 0 respectively:

+Line 1:

`o=7x-3\Rightarrow7x=3\Rightarrow x=(3)/(7)`

Its y-intercept is located at the point (3/7, 0)

`y=7(0)-3\Rightarrow y=-3`

Its x-intercept is located at the point (0, -3).

+Line 2:

`0=x+3\Rightarrow x=-3`

Its y-intercept is located at the point (-3, 0).

`y=(0)+3\Rightarrow y=3`

Its x-intercept is located at the point (0, 3).

**Now, using the x & y-intercepts of each line we plot the line using those points, as shown:

***

Since 3/7 is an irrational number it cannot be plotted by hand perfectly, so you can use another point of the line [Replace a value for y such that a solution is a number that can be plotted perfectly by hand] or you can use software to plot that point. I'll show you another point to plot it:

We can use y = 11 and we will get x = 2 (That is another point of the line that can be used to plot the line) [We use the x & y-intercepts since they are the immediate solutions most of the time, but any two points of the line can be used to plot it]. Look at the other point being used to plot it: