Answer:
Option b
Step-by-step explanation:
The following system of linear equations is shown
[tex]x + y = 8\\2x + y = 3[/tex]
These are two different slope lines.
We find the cut points of both lines with the axes.
[tex]x + y = 8[/tex]
Cut with the x axis. (y = 0)
[tex]x = 8[/tex]
Cut with the y axis. (x = 0)
[tex]y = 8[/tex]
...................................................................
[tex]2x + y = 3[/tex]
Cut with the x axis. (y = 0)
[tex]2x = 3\\x = 1.5[/tex]
Cut with the y axis. (x = 0)
[tex]y = 3[/tex]
The solution to this system will be a point for which it is fulfilled that:
[tex]x + y - 8 = 2x + y-3[/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 b is the only one that shows the graph of the lines
[tex]x + y = 8\\2x + y = 3[/tex]
Then, The point of intersection of both lines in the graph is:
(-5, 13)
Therefore the solution of the system of equations is: (-5, 13)
You can verify this by replacing the point in the relationship
[tex]x + y - 8 = 2x + y-3\\\\(-5) +13 -8 = 2 (-5) +13 -3\\\\0 = 0[/tex]
Equality is satisfied
Finally the answer is the option b
