Question

please help will give medals
how many solutions does the system of equations have 3x = -12y + 15 and x + 4y = 5

how many solutions does the system of equations have y = 6x + 2 and 3y - 18x = 12

how many solutions does the system of equations havex - 4y = 12 and 5x - 20y = 60

how many solutions does the system of equations have y - 6x = -3 and 4y - 24x = - 16

Answer 1

3x = - 12y + 15
3x + 12y = 15 reduces to x + 4y = 5
this matches the other equation, there, they are on the same line and have INFINITE SOLUTIONS
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y = 6x + 2
-6x + y = 2
6x - y = -2

3y - 18x = 12
-18x + 3y = 12
18x - 3y = -12 reduces to 6x - y = -4
The equations do not match, therefore, there is NO SOLUTION
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x - 4y = 12
5x - 20y = 60 reduces to x - 4y = 12
same equation, same line, INFINITE SOLUTIONS
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y - 6x = -3
-6x + y = -3
6x - y = 3

4y - 24x = -16
-24x + 4y = -16
24x - 4y = 16 reduces to 6x - y = 4
NO SOLUTIONS