Without graphing, determine the number of solutions of: $$\left\{ \begin{array} { l }
2 x - 4 y = 6 \
x + 2 y = - 3
\end{array} \right.$$
A)No solutions
B)One solution
C)Two solutions
D)Infinitely many solutions

Question

Without graphing, determine the number of solutions of: $$\left\{ \begin{array} { l } 
2 x - 4 y = 6 \
x + 2 y = - 3
\end{array} \right.$$
A)No solutions
B)One solution
C)Two solutions
D)Infinitely many solutions

Quizplus · Accepted Answer

We can solve this system of equations using substitution or elimination. If we use elimination, we can multiply the second equation by 2 and subtract it from the first equation to eliminate $y$:
$$2x - 4y - 2(x + 2y) = 6 - (-6)$$
Simplifying gives $-8y = 12$, or $y = -\frac{3}{2}$. Substituting this value for $y$ in the second equation gives:
$$x + 2\left(-\frac{3}{2}\right) = -3$$
Simplifying gives $x = 0$. Thus, there is one solution to the system of equations, namely $(0,-\frac{3}{2})$. Therefore, the answer is B.

Without Graphing, Determine the Number of Solutions Of {2x−4y=6x+2y=−3\left\{ \begin{array} { l } 2 x - 4 y = 6 \\x + 2 y = - 3\end{array} \right.{2x−4y=6x+2y=−3​

Without Graphing, Determine the Number of Solutions Of $\left\{ \begin{array} { l } 2 x - 4 y = 6 \\x + 2 y = - 3\end{array} \right.$