Question

Without solving, determine the number of solutions for the system of linear equations:

y=−10x+5
300=−15x+60y

a) One solution
b) No solution
c) Infinite solutions
d) Two solutions

Answer 1

The system of linear equations given has one solution because the ratios of the coefficients of x to y in both equations are different, indicating that the two lines will intersect at a single point.

Step-by-step explanation:

The system of linear equations given is:

• y = -10x + 5

• 300 = -15x + 60y

For the first equation, the coefficients are -10 for x and 1 for y. For the second equation, after dividing the entire equation by -15, the coefficients are 1 for x and -4 for y. Because the ratios of coefficients of x to y are different for the two equations (-10:1 versus 1:-4), it indicates the two lines will intersect at a single point. Therefore, the correct answer is: a) One solution.