Use the graph of the system to determine the solution. x + y = 4 x+ 3y= 6 What is the solution? Select the correct choice below and fill in an answer boxes in your choice.

A. (Type an ordered pair).
B. There are infinitely many solutions.
C. There is no solution.

Eq1: x + y = 4.

Eq2: 4x + 3y = 6.

Eq1: (-4,8), (4,0).
Eq2: (0,2), (3,-2).

Use the above points to graph the lines. The point of intersection is the
solution.

If your graph is correct, the solution
set will be: (-6,10).

To determine the solution of the system represented by the graph, we need to find the point where the two lines intersect.

From the equations given:

1) x + y = 4 (Equation 1)
2) x + 3y = 6 (Equation 2)

We can solve for x and y by using either substitution or elimination method. Let's use the elimination method:

First, multiply Equation 1 by 3 to make the coefficients of x in both equations equal:

3(x + y) = 3(4)
3x + 3y = 12 (Equation 3)

Now, subtract Equation 2 from Equation 3:

(3x + 3y) - (x + 3y) = 12 - 6
3x + 3y - x - 3y = 6
2x = 6
2x/2 = 6/2
x = 3

Substitute the value of x into either of the original equations (let's use Equation 1):

3 + y = 4
y = 4 - 3
y = 1

Therefore, the solution to the system of equations is the ordered pair (x, y) = (3, 1).

So, the correct choice is A. (Type an ordered pair). The solution is (3, 1).