Question

INSTRUCTIONS: Each of the pairs of linear equations in slope form will have either one solution (they intersect), no solution (they are parallel), or infinitely many solutions (they are the same thing). Based on the given slopes and intercepts, which are which?

y = 7x + 5 and y = 7x + 5
A. One Solution
B. No Solution
C. Infinite Solutions

y = 3x + 2 and y = 3x + 7
A. One Solution
B. No Solution
C. Infinite Solutions

y = 5x + 3 and y = 3x + 5
A. One Solution
B. No Solution
C. Infinite Solutions

Answer 1

The first pair of equations have infinite solutions, the second pair has no solution, and the third pair has one solution.

Step-by-step explanation:

The first pair of equations, y = 7x + 5 and y = 7x + 5, are the same equation. They have the same slope (7) and the same y-intercept (5). Therefore, they have infinite solutions.

The second pair of equations, y = 3x + 2 and y = 3x + 7, have the same slope (3) but different y-intercepts (2 and 7). Since they have different y-intercepts, the lines are parallel. Therefore, they have no solution.

The third pair of equations, y = 5x + 3 and y = 3x + 5, have different slopes (5 and 3) and different y-intercepts (3 and 5). Therefore, they intersect at exactly one point. Therefore, they have one solution.