Question

Solve for x and y in the system of equations: 6x−3y=−30 ,3x−6y=12

a) x=−5,y=−20
b) x=0,y=−10
c) x=2,y=12
d) x=4,y=18

Answer 1

To solve the system of equations 6x−3y=−30 and 3x−6y=12, we can use the method of elimination. The solution is x = -2 and y = 6.

Step-by-step explanation:

To solve the system of equations 6x−3y=−30 and 3x−6y=12, we can use the method of elimination. We can multiply the second equation by 2 to make the coefficients of y terms the same. Then, subtract the second equation from the first to eliminate y. This gives us 6x-3y - (6x-12y) = -30 - 24. Simplifying we get -9y = -54, or y = 6.

Substituting y=6 back into the first equation, we get 6x - 3(6) = -30. Simplifying we get 6x - 18 = -30, or 6x = -12. Solving for x, we get x = -2.

Therefore, the solution to the system of equations is x = -2 and y = 6. So option (a) is the correct answer.