What is the solution of the system?Use the substitution method.{y+7=3x6x−2y=12 (14, 12) (12, 14) There is no solution. There are an infinite number of solutions.
Accepted Solution
A:
Answer: Choice C) no solutions=============================Work Shown:y+7 = 3x turns into y = 3x-7 after we subtract 7 from both sidesPlug that into the other equation and solve for x------6x - 2y = 126x - 2( y ) = 126x - 2( 3x-7 ) = 12 ... y replaced with 3x-76x - 2(3x) - 2(-7) = 126x - 6x + 14 = 120x + 14 = 120 + 14 = 1214 = 12 ... this is a contradiction, aka false statement------No matter what x value we pick, the equation above will always be false.Therefore, there are no solutionsWe say that this system of equations is inconsistent.Graphing both equations leads to two parallel lines. A solution only happens if the lines cross, but parallel lines never intersect.