y = 5x + 7

3y - 15x = 18

does this have one solution or no solutions or infinite solutions

1 answer

To determine the number of solutions, we can use the method of solving a system of linear equations. We can rewrite the first equation as 5x - y = -7.

Now we have the following system of equations:

5x - y = -7 ...(1)
3y - 15x = 18 ...(2)

To solve this system, we can multiply equation (1) by 3 to make the coefficients of "y" in both equations the same:

15x - 3y = -21 ...(3)
3y - 15x = 18 ...(2)

Combining equations (2) and (3) will eliminate the "x" terms:

(3y - 15x) + (15x - 3y) = 18 + (-21)
0 = -3

Since we get an inconsistent equation (0 = -3), it means that there is no solution to this system of equations. Therefore, the original equations y = 5x + 7 and 3y - 15x = 18 do not have a solution.