Question

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how many solutions does the system of equations below have? 8x + 4y = -5 16x + 8y = -5 no solution one solution infinitely many solutions

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation $8x + 4y=-5$, solve for $y$:
$4y=-8x - 5$, so $y=-2x-\frac{5}{4}$.
For the second equation $16x + 8y=-5$, solve for $y$:
$8y=-16x - 5$, so $y=-2x-\frac{5}{8}$.

Step2: Analyze slopes and y - intercepts

The slope of the first line $m_1=-2$ and y - intercept $b_1 =-\frac{5}{4}$.
The slope of the second line $m_2=-2$ and y - intercept $b_2=-\frac{5}{8}$.
Since the slopes are equal ($m_1 = m_2=-2$) and the y - intercepts are different ($b_1
eq b_2$), the lines are parallel.

Answer:

no solution