Question

Solve the systems of equation by graphing (Picture provided)

Answer 1

Answer:

Option b

Step-by-step explanation:

The following system of linear equations is shown

$x + y = 8\\2x + y = 3$

These are two different slope lines.

We find the cut points of both lines with the axes.

$x + y = 8$

Cut with the x axis. (y = 0)

$x = 8$

Cut with the y axis. (x = 0)

$y = 8$

...................................................................

$2x + y = 3$

Cut with the x axis. (y = 0)

$2x = 3\\x = 1.5$

Cut with the y axis. (x = 0)

$y = 3$

The solution to this system will be a point for which it is fulfilled that:

$x + y - 8 = 2x + y-3$

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

$x + y = 8\\2x + y = 3$

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

$x + y - 8 = 2x + y-3\\\\(-5) +13 -8 = 2 (-5) +13 -3\\\\0 = 0$

Equality is satisfied

Finally the answer is the option b