Answer:
Option d
Step-by-step explanation:
The following system of linear equations is shown
[tex]x + y = -7\\4x + y = 19[/tex]
These are two different slope lines.
We find the cut points of both lines with the axes.
[tex]x + y = -7[/tex]
Cut with the x axis. (y = 0)
[tex]x = -7[/tex]
Cut with the y axis. (x = 0)
[tex]y = -7[/tex]
...............................................................................................................................
[tex]4x + y = 19[/tex]
Cut with the x axis. (y = 0)
[tex]4x = 19[/tex]
[tex]x = 4.75[/tex]
Cut with the y axis. (x = 0)
[tex]y = 19[/tex]
The solution to this system will be a point for which it is fulfilled that:
[tex]x + y +7 = 4x + y-19[/tex]
In the image, different graphs with intersections are shown.
Locate among the options, one that shows the two lines of the system of equations according to their intersections with the x and y axes.
Option d is the only one that shows the graph of the lines
[tex]x + y = -7\\4x + y = 19[/tex]
Then, The point of intersection of both lines in the graph is:
(8.7, -15.7)
Therefore the solution of the system of equations is: (8.7, -15.7)
You can verify this by replacing the point in the relationship
[tex]x + y +7 = 4x + y-19\\(8.7) -15.7 +7 = 4(8.7) -15.7 -19\\0 = 0[/tex]
Equality is satisfied
The answer is the option d.
