how many solutions does the system of equations have?
y=6x+2
3y-18x=12
To determine the number of solutions for the system of equations, we can solve the equations by substitution or elimination.
1) Solving by substitution:
Substitute the expression for y from the first equation into the second equation:
3(6x + 2) - 18x = 12
18x + 6 - 18x = 12
6 = 12
The equation 6 = 12 is false, indicating there is no solution to this system of equations. Hence, the system of equations has 0 solutions.
2) Solving by elimination:
Multiply the first equation by 3 to make the coefficients of y in both equations equal:
3y - 18x = 6y + 6
-18x - 3y = 6
Simplifying the equations, we have:
-18x - 3y = 6
From this equation, we can see that there is no information about x. It is impossible to determine a specific solution for the system of equations. Therefore, the system has 0 solutions.