Question

graph the system below and write its solution.$\begin{cases} y=\frac{1}{2}x - 1 \\ 3x+y=6 end{cases}$note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

Step1: Rearrange second equation

Rewrite $3x+y=6$ to slope-intercept form:
$y = -3x + 6$

Step2: Set equations equal

Since both equal $y$, equate them:
$\frac{1}{2}x - 1 = -3x + 6$

Step3: Solve for $x$

Multiply all terms by 2 to eliminate fraction:
$x - 2 = -6x + 12$
$x + 6x = 12 + 2$
$7x = 14$
$x = 2$

Step4: Find $y$ value

Substitute $x=2$ into $y=\frac{1}{2}x -1$:
$y = \frac{1}{2}(2) - 1 = 1 - 1 = 0$

Step5: Verify solution

Check in $3x+y=6$:
$3(2) + 0 = 6$, which is true.

Answer:

The solution is $(2, 0)$
(To graph: Plot $y=\frac{1}{2}x-1$ using y-intercept $(0,-1)$ and slope $\frac{1}{2}$; plot $y=-3x+6$ using y-intercept $(0,6)$ and slope $-3$. The lines intersect at $(2,0)$.)