Question

-2x+3y=3
x-6y=12
A.
(–6, –3)
B.
(–3, –6)
C.
(3, 6)
D.
(6, 3)

Answer 1

Could solve this by elimination or substitution.
Substitution:
Rearrange one of the formulas to give one of the variables in terms of the other. \[x-6y=12\]\[x=6y+12\]Now substitute that wherever you see x in the other equation and solve for y:
\[-2(6y+12)+3y=3\]\[-12y-24+3y=3\]\[-9y=27\]
Go back to the original equation and substitute the value you found for y and use that to solve for x.

Elimination:
Multiply or divide one of the equations by a number that will cause one of the variables to drop out when you add or subtract the equations. Solve for the value of the remaining variable, then proceed similarly to how you finished with substitution method.

In this case, if we multiply the second equation by 2, the x terms will cancel out when the equations are added:
\[-2x+3y + 2(x-6y) = 3 + 2(12)\]\[-2x + 3y + 2x -12y = 3 + 24\]\[3y - 12y =27\]\[-9y = 27\]