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

is this a new one or the same one...Step-by-step explanation:...

Choose the graph that matches the following system

amandajennings01

12.01.2022

Graph A is correct.

Step-by-step explanation:

We are given the system of inequality,

$x+y=4\\\\2x+3y=18$

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

We have the equations,

x + y = 4 ............(1)

2x + 3y = 18 .............(2)

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

$2x+2y-2x-3y=8-18\\-y=-10\\y=10$

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

$x + 10 = 4\\x=4-10\\x=-6$

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,

y=-x+4

$y =\frac{-2}{3}x+6$

Thus, the slope of the equations are -1 and $\frac{-2}{3}$ .

Then, the graphs of the equations must be decreasing.

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

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