Question

Which graph represents the solution to the given system negative 2x + 3y = -18 and 4x - y = -1

Answer 1

In order to graph the system of equations, we can convert them into slope-intercept form, y = mx + b.

For the equation -2x + 3y = -18:
3y = 2x - 18
y = (2/3)x - 6

For the equation 4x - y = -1:
-y = -4x - 1
y = 4x + 1

Now we can graph these equations to find the solution.

Graph 1: y = (2/3)x - 6
This line has a slope of (2/3) and y-intercept of -6.
Start by plotting the y-intercept at (0, -6), and then use the slope to draw the line.
Here is the graph of equation 1:
{{{ graph( 300, 200, -10, 10, -10, 10, (2/3)x - 6) }}}

Graph 2: y = 4x + 1
This line has a slope of 4 and y-intercept of 1.
Start by plotting the y-intercept at (0, 1), and then use the slope to draw the line.
Here is the graph of equation 2:
{{{ graph( 300, 200, -10, 10, -10, 10, 4x + 1) }}}

The solution to the system of equations is represented by the point where the two lines intersect. From the graph, we can see that the lines intersect at the point (-3, -11).

So, the correct graph representing the solution to the given system is:
Answer: graph with the point (-3, -11)