Question

Consider the following system of equations. − 2 ⁢ x + 5 ⁢ y = 19 y = − 5 6 ⁢ x − 1 6 Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. ( − 13 4 , 5 2 ) B. ( 5 2 , − 13 4 ) C. ( 13 4 , − 5 2 ) D. ( − 5 2 , 13 4 )

Answer 1

Approximate solution of the system is:

B. (5/2, -13/4)

Explanation:

To approximate the solution of the given system of equations using the graph, we need to find the point where the two lines intersect. Let's analyze the equations and the graph to determine the approximate solution.

The given system of equations is:

-2x + 5y = 19 ...(1)

y = (-5/6)x - (1/6) ...(2)

Looking at equation (2), we can see that it represents a diagonal line with a negative slope, passing through the points (-5, 1) and (6, 6).

Now let's plot this line on the graph:

|

6 | x

|

| x

5 | x

|

| x

4 |

|

3 |

|

2 |

|

1 | x

|

0 |____________________

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

The line rises from (-5, 1) to (6, 6).

Next, let's analyze equation (1), which can be rearranged as:

5y = 2x + 19

y = (2/5)x + (19/5)

Comparing equation (1) with equation (2), we can see that the slope of the line in equation (1) is positive, and it intersects the other line at a point. Therefore, we are looking for the point where the rising diagonal line intersects the line with a positive slope.

By visually examining the graph, we can approximate the intersection point to be around (5/2, -13/4).

Hence, the approximate solution of the system is:

B. (5/2, -13/4)