Part A
Rewrite the following system of equations in slope intercept form. The system of equation is:
- 6x + u = 10
- 36x + 6y = 48
- 6x = 10 - y - 36x = 48 - 6y
y = 6x + 10 y = 6x + 8
y = 6x + 10 y = 36x + 48
None of the above
Part B
From the above slope intercept forms of the system of equations, the system has (Infinite Solutions, None of the Above, No Solution, One Solution) Match the Graphs with their solutions. Each Graph has two linear equations graphed.
Part A:
To rewrite the system of equations in slope-intercept form:
-6x + u = 10
First, isolate the variable u:
u = 6x + 10
Next, rewrite the second equation in slope-intercept form:
36x + 6y = 48
Divide both sides of the equation by 6:
6y = -36x + 48
Divide both sides of the equation by 6:
y = -6x + 8
So the equations in slope-intercept form are:
u = 6x + 10
y = -6x + 8
Therefore, the correct answer is "None of the above."
Part B:
Since the system of equations has been rewritten in slope-intercept form as:
u = 6x + 10
y = -6x + 8
We can match the graphs with their solutions as follows:
Graph 1: y = -6x + 8
Graph 2: u = 6x + 10
The system of equations has one solution, where the two lines intersect at a single point on the graph.
Therefore, the correct answer is "One Solution - The graphs intersect at a single point."