Part A
Rewrite the following system of equations in slope intercept form. The system of equation is:
- 6x + u = 10
- 36x + 6y = 48
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. (4 points)
Part A:
To rewrite the system of equations in slope-intercept form, we need to solve each equation for y.
1) -6x + u = 10
Subtract u from both sides:
-6x = 10 - u
Divide both sides by -6:
x = (10 - u)/-6
2) 36x + 6y = 48
Subtract 36x from both sides:
6y = 48 - 36x
Divide both sides by 6:
y = (48 - 36x)/6
Simplify:
y = 8 - 6x/6
y = 8 - x
Part B:
From the slope-intercept forms obtained in Part A:
1) For the equation x = (10 - u)/-6, the line is vertical with x-intercept equal to (10 - u)/-6. This line will have one solution.
2) For the equation y = 8 - x, the line has a slope of -1 and a y-intercept of 8. This line will have one solution.
The system of equations has One Solution.
To match the graphs with their solutions, we need the graphs of two lines intersecting at one point.