Question

Solve the systems of equation by graphing (Picture provided)

Answer 1

Option d

Explanation:

The following system of linear equations is shown

`x + y = -7\\4x + y = 19`

These are two different slope lines.

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

`x + y = -7`

Cut with the x axis. (y = 0)

`x = -7`

Cut with the y axis. (x = 0)

`y = -7`

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

`4x + y = 19`

Cut with the x axis. (y = 0)

`4x = 19`

`x = 4.75`

Cut with the y axis. (x = 0)

`y = 19`

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

`x + y +7 = 4x + y-19`

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

`x + y = -7\\4x + y = 19`

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

`x + y +7 = 4x + y-19\\(8.7) -15.7 +7 = 4(8.7) -15.7 -19\\0 = 0`

Equality is satisfied

The answer is the option d.