solve each system graphically. be sure to check your solution. if a system has an infinite number of…

Explanation:

Step1: Rewrite equations in slope - intercept form

The first equation $s=t + 9$ is already in slope - intercept form $y=mx + b$ (where $s$ is like $y$ and $t$ is like $x$) with slope $m = 1$ and $y$ - intercept $b = 9$. The second equation $t+3s=-1$ can be rewritten as $3s=-t - 1$ or $s=-\frac{1}{3}t-\frac{1}{3}$. Here the slope is $-\frac{1}{3}$ and the $y$ - intercept is $-\frac{1}{3}$.

Step2: Find the intersection point

Set the two equations equal to each other: $t + 9=-\frac{1}{3}t-\frac{1}{3}$. Add $\frac{1}{3}t$ to both sides: $t+\frac{1}{3}t+9=-\frac{1}{3}$. Combine like terms: $\frac{3t + t}{3}+9=-\frac{1}{3}$, so $\frac{4t}{3}+9=-\frac{1}{3}$. Subtract 9 from both sides: $\frac{4t}{3}=-\frac{1}{3}-9=-\frac{1 + 27}{3}=-\frac{28}{3}$. Multiply both sides by $\frac{3}{4}$: $t=-\frac{28}{3}\times\frac{3}{4}=-7$. Substitute $t = - 7$ into the first equation $s=t + 9$, then $s=-7 + 9=2$.

Answer:

The solution of the system is the ordered pair $(-7,2)$