graph represents the system of equation The correct answer is x³ - 64 = (x - 4) (x² + 4x + 16) correct answer.
To determine which graph represents the system of equations, let's convert the inequalities to slope-intercept form and plot the lines:
Equation 1: Y > (-1/3)X + 4
This equation represents a line with a slope of -1/3 and a y-intercept of 4. We can plot the line by starting at the point (0, 4) and extending it downwards.
Equation 2: 2X - 3Y ≤ 12
This inequality can be rewritten in slope-intercept form as:
Y ≤ (2/3)X - 4
This equation represents a line with a slope of 2/3 and a y-intercept of -4. We can plot the line by starting at the point (0, -4) and extending it upwards.
Shading the Area:
Since the first inequality (Y > (-1/3)X + 4) requires Y to be greater than the line, we shade the area above the line.
For the second inequality (Y ≤ (2/3)X - 4), we shade the area below the line.
Identifying the Correct Graph:
Comparing the shaded areas of the equations to the given graphs, we can see that Graph 3 correctly represents the system of equations. This graph shows the shaded area above the line Y > (-1/3)X + 4 and below the line Y ≤ (2/3)X - 4, satisfying both inequalities.
Therefore, Graph 3 represents the system of equations Y > (-1/3)X + 4 and 2X - 3Y ≤ 12.
complete the question
Which graph represents the system of equations?
Y > (-1/3)X + 4
2X - 3Y ≤ 12