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.
-$$\begin{array} { l }
\frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \
\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2
\end{array}$$
A) $( 0,12 )$
B) $\left( - 1 , \frac { 15 } { 2 } \right)$
C) $\left( x , - \frac { 3 } { 2 } x + 12 \right)$ or $\left( - \frac { 2 } { 3 } y + 8 , y \right)$
D) no solution

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.
-$$\begin{array} { l } 
\frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \
\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2
\end{array}$$
A) $( 0,12 )$
B) $\left( - 1 , \frac { 15 } { 2 } \right)$
C) $\left( x , - \frac { 3 } { 2 } x + 12 \right)$ or $\left( - \frac { 2 } { 3 } y + 8 , y \right)$
D) no solution

Quizplus · Accepted Answer

The system of equations is equivalent when both equations are multiplied by a constant to make them identical, indicating infinitely many solutions. Multiplying the second equation by 2 yields the same equation as the first, thus the solutions can be expressed in terms of either variable.

Use the Substitution Method or the Elimination Method to Solve 12x+13y=414x+16y=2\begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \\\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2\end{array}21​x+31​y=441​x+61​y=2​

Use the Substitution Method or the Elimination Method to Solve $\begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \\\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2\end{array}$