y = -\\frac{1}{2}x + 4\nx + 2y = -8\nhow many solutions does this linear system have?\none solution: (8…

y = -\\frac{1}{2}x + 4\nx + 2y = -8\nhow many solutions does this linear system have?\none solution: (8, 0)\none solution: (0, 8)\nno solution\ninfinite number of solutions

y = -\\frac{1}{2}x + 4\nx + 2y = -8\nhow many solutions does this linear system have?\none solution: (8, 0)\none solution: (0, 8)\nno solution\ninfinite number of solutions

Answer

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

Starting with $x + 2y=-8$, solve for $y$. First, subtract $x$ from both sides: $2y=-x - 8$. Then divide by 2: $y=-\frac{1}{2}x-4$.

Step2: Compare the slopes and y - intercepts

The first equation is $y =-\frac{1}{2}x + 4$, and the second equation is $y=-\frac{1}{2}x-4$. The slopes of both lines are $m =-\frac{1}{2}$, but the y - intercepts are $b_1 = 4$ and $b_2=-4$. Since the slopes are equal and the y - intercepts are different, the lines are parallel.

Answer:

no solution