Question

Which of the following is not a solution to the system of linear equations below?

Answer 1

Answer:

B. (-15, 12)

Step-by-step explanation:

$\left\{\begin{array}{ccc}5y=3x+15&\text{subtract 3x from both sides}\\6x=10y-30&\text{subtract 10y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3x+5y=15\\6x-10y=-30&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+5y=15\\3x-5y=-15\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}\\\\\bold{Infinitely\ many\ solutions}\\\\5y=3x+15\qquad\text{divide both sides by 5}\\\\y=\dfrac{3}{5}x+3\qquad(*)\\\\\text{Put the coordinates of the points to the equation (*)}$

$A.\ (5,\ 6)\\\\6=\dfrac{3}{5}(5)+3\\\\6=3+3\\\\6=6\qquad\bold{CORRECT}\\\\B.\ (-15,\ 12)\\\\12=\dfrac{3}{5}(-15)+3\\\\12=(3)(-3)+3\\\\12=-9+3\\\\12=-6\qquad\bold{FALSE}\\\\C.\ (0,\ 3)\\\\3=\dfrac{3}{5}(0)+3\\\\3=0+3\\\\3=3\qquad\bold{CORRECT}\\\\D.\ (-10,\ -3)\\\\-3=\dfrac{3}{5}(-10)+3\\\\-3=(3)(-2)+3\\\\-3=-6+3\\\\-3=-3\qquad\bold{CORRECT}$