Question

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how many solutions does the system of equations below have?
$x + 4y = 10$
$4x + 16y = 13$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation $x + 4y=10$, we can rewrite it as $y=-\frac{1}{4}x+\frac{10}{4}=-\frac{1}{4}x + 2.5$. For the second equation $4x + 16y=13$, we first divide through by 4 to get $x + 4y=\frac{13}{4}$, then rewrite it as $y=-\frac{1}{4}x+\frac{13}{16}$.

Step2: Analyze the slopes and y - intercepts

The slopes of both lines are $m =-\frac{1}{4}$. The y - intercepts are $b_1 = 2.5$ and $b_2=\frac{13}{16}$. Since the slopes are equal and the y - intercepts are different, the lines are parallel.

Answer:

no solution