solve the following system of equations graphically on the set of axes below.$y = x + 1$$y = -\frac{1}{3}x +…

Explanation:

Step1: Find intercepts for $y=x+1$

• y-intercept: When $x=0$, $y=0+1=1$, so point $(0,1)$.
• x-intercept: When $y=0$, $0=x+1 \implies x=-1$, so point $(-1,0)$.

Step2: Find intercepts for $y=-\frac{1}{3}x+5$

• y-intercept: When $x=0$, $y=0+5=5$, so point $(0,5)$.
• x-intercept: When $y=0$, $0=-\frac{1}{3}x+5 \implies \frac{1}{3}x=5 \implies x=15$, so point $(15,0)$.

Step3: Find intersection algebraically

Set $x+1 = -\frac{1}{3}x+5$ Multiply all terms by 3: $3x+3 = -x+15$ Combine like terms: $3x+x=15-3$ $4x=12 \implies x=3$ Substitute $x=3$ into $y=x+1$: $y=3+1=4$

Answer:

The solution to the system is the intersection point $(3, 4)$. To graph:

1. Draw a line through $(-1,0)$ and $(0,1)$ for $y=x+1$.
2. Draw a line through $(0,5)$ and $(15,0)$ for $y=-\frac{1}{3}x+5$.
3. The lines cross at $(3, 4)$.