y=4x-8
4y=4x-8
A. One solution
B . No solutions
C . Many solutions
4y=4x-8
/4 /4
y=x-2
x= the slope
-2= y intercept
A
y=4x-8
4y=4x-8
so,
y = 4y
y = 0
x = 2
A is correct, but it's the x-intercept.
To determine the number of solutions for the given system of equations, we need to compare their slopes and y-intercepts.
Let's analyze the equations:
1) y = 4x - 8
This equation is in slope-intercept form (y = mx + b), where m represents the slope (4) and b represents the y-intercept (-8).
2) 4y = 4x - 8
This equation can be rearranged to slope-intercept form by dividing both sides by 4:
y = (4/4)x - 8/4
Which simplifies to:
y = x - 2
Comparing the slopes and y-intercepts:
The slope of equation 1 (y = 4x - 8) is 4, and the slope of equation 2 (y = x - 2) is 1. Since the slopes are different, the lines are not parallel, and they will intersect at a single point.
The y-intercepts of both equations are different (-8 and -2), indicating that the lines do not intersect at the y-axis.
Based on this analysis, we can conclude that the system of equations has A. One solution.
To determine the number of solutions for this system of equations, let's analyze the equations:
Equation 1: y = 4x - 8
Equation 2: 4y = 4x - 8
For both equations, the right side (4x - 8) is the same.
Now let's simplify Equation 2 by dividing both sides by 4:
(4y) / 4 = (4x - 8) / 4
Simplifying further, we get:
y = x - 2
Comparing both equations, we can see that they are equivalent. Equation 1 is in slope-intercept form, while Equation 2 is in standard form. When we simplify Equation 2, we obtain Equation 1. Therefore, these equations represent the same line.
When two equations represent the same line, they have infinite points of intersection, which means they have infinite solutions. Each point on the line represents a solution common to both equations.
Therefore, the answer is C. Many solutions.