Final answer:
The equation that would result in infinitely many solutions when part of a system with the given equation 5x - 2y = 8 is option c) 5x - 2y = 8, because it represents the same line with identical slope and y-intercept.
Step-by-step explanation:
In order for a pair of linear equations to have infinitely many solutions, they must represent the same line; that is, they must have the same slope and y-intercept. Let's rewrite the given equation 5x - 2y = 8 into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, solve for y:
- 5x - 2y = 8 (original equation)
- -2y = -5x + 8 (subtract 5x from both sides)
- y = (5/2)x - 4 (divide both sides by -2 to solve for y)
The slope-intercept form of the given equation is y = (5/2)x - 4. Now, let's examine the options:
- a) y = 5x - 8
- b) y = 2x + 4
- c) 5x - 2y = 8
- d) 3x + y = 4
Option c) is the correct answer because it is the same as the original equation, and thus it has the same slope and y-intercept, resulting in infinitely many solutions when paired with the original equation as part of a system.