solve the following system of equations graphically on the set of axes below.\n$y = -x + 5$\n$y =…

solve the following system of equations graphically on the set of axes below.\n$y = -x + 5$\n$y = \\frac{1}{2}x - 4$\nplot two lines by clicking the graph.\nclick a line to delete it.

solve the following system of equations graphically on the set of axes below.\n$y = -x + 5$\n$y = \\frac{1}{2}x - 4$\nplot two lines by clicking the graph.\nclick a line to delete it.

Answer

Explanation:

Step1: Find intercepts for $y=-x+5$

  • y-intercept: When $x=0$, $y=5$ → point $(0,5)$
  • x-intercept: When $y=0$, $0=-x+5 \implies x=5$ → point $(5,0)$

Step2: Find intercepts for $y=\frac{1}{2}x-4$

  • y-intercept: When $x=0$, $y=-4$ → point $(0,-4)$
  • x-intercept: When $y=0$, $0=\frac{1}{2}x-4 \implies x=8$ → point $(8,0)$

Step3: Find intersection algebraically

Set equations equal: $$-x+5 = \frac{1}{2}x-4$$ Multiply all terms by 2 to eliminate fraction: $$-2x+10 = x-8$$ Rearrange to solve for $x$: $$10+8 = x+2x \implies 18=3x \implies x=6$$ Substitute $x=6$ into $y=-x+5$: $$y=-6+5=-1$$

Answer:

The solution to the system is the point $(6, -1)$. To graph:

  1. Plot $(0,5)$ and $(5,0)$, draw the line for $y=-x+5$.
  2. Plot $(0,-4)$ and $(8,0)$, draw the line for $y=\frac{1}{2}x-4$.
  3. The lines intersect at $(6, -1)$.