Solve the system by elimination.
-8x - 3y = 22 3x + 8y = 63
A) (5, 6)
B) No solution
C) (-2, -7)
D) (-5, 6)

Question

Quizplus · Accepted Answer

To solve the system by elimination, we aim to eliminate one of the variables by adding or subtracting the equations. First, we can multiply the first equation by 8 and the second equation by 3 to make the coefficients of y equal (with opposite signs):First equation: $8x - 3y = 22$ becomes $64x - 24y = 176$ (multiplied by 8)Second equation: $3x + 8y = 63$ becomes $9x + 24y = 189$ (multiplied by 3)Adding these equations together to eliminate y gives:$64x + 9x = 176 + 189$$73x = 365$$x = 5$Substitute $x = 5$ into one of the original equations to find y. Using the first equation:$8(5) - 3y = 22$$40 - 3y = 22$$-3y = -18$$y = 6$Therefore, the solution is $x = 5, y = 6$, which corresponds to choice A.

Solve the System by Elimination