5. Solve the system of equations by the method of your choice. ) 4x+y=16 16x+4y=64 A) (5,-4) B) (0,16) C) Infinitely Many D) varnothing

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method for this problem:<br /><br />The given system of equations is:<br />\[<br />\begin{cases} <br />4x + y = 16 \\<br />16x + 4y = 64 <br />\end{cases}<br />\]<br /><br />First, let's simplify the second equation by dividing every term by 4:<br />\[<br />16x + 4y = 64 \implies 4x + y = 16<br />\]<br /><br />Now, notice that both equations are identical:<br />1. \(4x + y = 16\)<br />2. \(4x + y = 16\)<br /><br />Since both equations represent the same line, there are infinitely many solutions (every point on the line is a solution).<br /><br />Therefore, the correct answer is:<br />C) Infinitely Many