{:[6x+2y=3],[6x+y=3]:} Consider the given system of equations. How many (x,y) solutions does this system have? Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions (D) None of the above

Question

{:[6x+2y=3],[6x+y=3]:} Consider the given system of equations. How many  (x,y) solutions does this system have? Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions (D) None of the above

Bytelearn · Accepted Answer

Analyze System of Equations: Let's analyze the system of equations: $$ \begin{cases}  6x + 2y = 3 \ 6x + y = 3  \end{cases} $$ We will subtract the second equation from the first to eliminate the variable x and find the value of y.Subtract to Eliminate Variable: Subtracting the second equation from the first gives us: $$ (6x + 2y) - (6x + y) = 3 - 3 $$ $$ 6x + 2y - 6x - y = 0 $$ $$ 2y - y = 0 $$ $$ y = 0 $$Find Value of y: Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the second equation: $$ 6x + y = 3 $$ $$ 6x + 0 = 3 $$ $$ 6x = 3 $$ $$ x = \frac{3}{6} $$ $$ x = \frac{1}{2} $$Substitute to Find x: We have found a single solution for the system of equations: $ x = \frac{1}{2} $ and $ y = 0 $. This means that the system has exactly one solution.

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