To identify the correct graph of the system of equations, we need to solve the equations and determine their intersection point.
Let's solve the system of equations:
1. 3x + y = 12
2. x + 4y = 4
We can solve this system of equations using various methods such as substitution or elimination. Let's use the elimination method here:
Multiply equation 1 by 4 and equation 2 by 1 to eliminate the y term:
1. 12x + 4y = 48
2. x + 4y = 4
Now, subtract equation 2 from equation 1:
12x + 4y - (x + 4y) = 48 - 4
Simplifying:
11x = 44
Divide both sides by 11:
x = 4
Substitute the value of x into equation 2 to solve for y:
4 + 4y = 4
4y = 4 - 4
4y = 0
y = 0
Therefore, the solution to the system of equations is x = 4 and y = 0.
The correct graph of this system of equations would be two lines intersecting at the point (4, 0) on the coordinate plane.