Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
Unfortunately, as an AI language model, I cannot generate images. However, I can describe the correct graph of the system of equations.
The correct graph is two straight lines that intersect at a single point. The point of intersection represents the solution to the system of equations.
To identify the correct graph of the system of equations, we need to find the solution to the system by graphing both equations on the same coordinate grid.
First, let's rewrite the equations in slope-intercept form (y = mx + b).
For the first equation, 3x + y = 12, we need to isolate y:
y = -3x + 12
For the second equation, x + 4y = 4, isolate y:
4y = -x + 4
y = (-1/4)x + 1
Now, we can graph the equations:
The graph of the first equation, y = -3x + 12, has a y-intercept of 12 and a slope of -3. This means we can start at the point (0, 12) on the y-axis and from there, move downward 3 units for every 1 unit we move to the right.
The graph of the second equation, y = (-1/4)x + 1, has a y-intercept of 1 and a slope of -1/4. This means we can start at the point (0, 1) on the y-axis and from there, we move downward 1 unit for every 4 units we move to the right.
Now, let's plot the points and draw the lines:
Graph:
Here, the lines intersect at the point (4, 0). This is the solution to the system of equations.
Therefore, the correct graph of the system of equations is a point at (4, 0), where the two lines intersect.