Choose the graph that matches the following system of equations:
x + y = 4
2x + 3y = 18

Step-by-step explanation:

We are given the system of inequality,

Now, it is required to find the graph of the system of equations.

We have the equations,

        ............(1)

 .............(2)

Multiplying (1) by 2 and subtracting the equations gives us,

Substituting the value of y in any equation, we get,

Thus, the solution of the system of equations is (-6,10).

As we have that the point (-6,10) will lie in the second quadrant.

So, the graphs of the equations must intersect in the second quadrant.

Moreover, the slope intercept forms of the equations are given by,

Thus, the slope of the equations are -1 and .

Then, the graphs of the equations must be decreasing.

Hence, the correct option is 'Graph A' given below.

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4