SOLUTION: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -3x+4y=1 -6x+6y=-3

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Question 624398: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x+4y=1
-6x+6y=-3
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
multiply both sides of the first equation by -2 to get:
6x - 8y = -2
add the second equation to the first equation to get:
6x - 8y = -2
plus:
-6x + 6y = -3
equals:
-2y = -5
divide both sides by -2 to get:
y = 5/2
substitute for y in second equation to get:
-6x + 6(5/2) = -3
simplify to get:
-6x + 15 = -3
subtract 15 from both sides of the equation to get:
-6x = -18
divide both sides by -6 to get:
x = 3
you have:
x = 3
y = 5/2
substitute in first original equation to get:
-3x+4y=1 becomes:
-3(3) + 4(5/2) = 1 which simplifies to:
-9 + 20/2 = 1 which further simplifies to:
-9 + 10 = 1
subtract 10 from both sides of this equation to get:
-9 = -9 confirming that x = 3 and y = 5/2 are solutions to the system of equations.