solve the following system of equations graphically on the set of axes below.\n$y = -x + 5$\n$y = 2x…

Explanation:

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

Y-intercept: when $x=0$, $y=5$ → $(0,5)$ X-intercept: when $y=0$, $0=-x+5$ → $x=5$ → $(5,0)$

Step2: Plot $y=-x+5$

Draw line through $(0,5)$ and $(5,0)$

Step3: Find intercepts for $y=2x-1$

Y-intercept: when $x=0$, $y=-1$ → $(0,-1)$ X-intercept: when $y=0$, $0=2x-1$ → $x=\frac{1}{2}$ → $(0.5,0)$

Step4: Plot $y=2x-1$

Draw line through $(0,-1)$ and $(0.5,0)$

Step5: Find intersection point

Set $-x+5=2x-1$ → $5+1=2x+x$ → $6=3x$ → $x=2$ Substitute $x=2$ into $y=-x+5$: $y=-2+5=3$ Intersection: $(2,3)$

Answer:

The solution to the system is the point of intersection $\boldsymbol{(2, 3)}$ (To complete the graph: plot the line $y=-x+5$ through $(0,5)$ and $(5,0)$, plot the line $y=2x-1$ through $(0,-1)$ and $(0.5,0)$, their intersection is $(2,3)$)