Q:

# Choose the graph that matches the following system of equations: 2x + y = −1 3x + 2y = −6Select one:a. picture of coordinate plane with line y equals negative 2x plus 1 and line y equals 3 halves x minus 6. They intersect at 2, negative 3b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9c. picture of coordinate plane with line y equals 2x minus 1 and line y equals negative 3x minus 3. They intersect at negative 0.4, negative 1.8d. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals 3 halves x plus 6. They intersect at negative 2, 3

Accepted Solution

A:
Hi! You don't actually need to graph this nor find the intersection in order to know the answer. Through the process of elimination we can rule out incorrect answers.

Firstly, we express both equations with y on the left hand side since all choices are in that form:

$$y=-2x-1$$
$$y=- \frac{3}{2}x-3$$

Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.

You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).

ANSWER: b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.