Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-3x + y = 6 -6x - 2y = -12
A) $( x , - 3 x + 6 )$ or $\left( - \frac { 1 } { 3 } y + 2 , y \right)$
B) $( x , 3 x + 6 )$ or $\left( \frac { 1 } { 3 } y - 2 , y \right)$
C) no solution
D) $\left( - \frac { 1 } { 3 } x + 2 , x \right)$ or $( y , - 3 y + 6 )$

Question

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-3x + y = 6 -6x - 2y = -12 
A) $( x , - 3 x + 6 )$ or $\left( - \frac { 1 } { 3 } y + 2 , y \right)$
B) $( x , 3 x + 6 )$ or $\left( \frac { 1 } { 3 } y - 2 , y \right)$
C) no solution
D) $\left( - \frac { 1 } { 3 } x + 2 , x \right)$ or $( y , - 3 y + 6 )$

Quizplus · Accepted Answer

The second equation is -2 times the first, indicating the same line, hence infinitely many solutions. The expressions for y in terms of x and x in terms of y are correctly given in option A.

Use the Substitution Method or the Elimination Method to Solve (x,−3x+6)( x , - 3 x + 6 )(x,−3x+6)

Use the Substitution Method or the Elimination Method to Solve $( x , - 3 x + 6 )$