Question

graph the system
$\

$$\begin{cases} y=3x-1 \\\\ x-2y=7 \\end{cases}$$

$
note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Solve $x-2y=7$ for $y$:
Subtract $x$ from both sides: $-2y = -x + 7$
Divide by $-2$: $y = \frac{1}{2}x - \frac{7}{2}$

Step2: Find intersection via substitution

Substitute $y=3x-1$ into $y = \frac{1}{2}x - \frac{7}{2}$:
$$3x - 1 = \frac{1}{2}x - \frac{7}{2}$$
Multiply all terms by 2 to eliminate fractions:
$$6x - 2 = x - 7$$
Subtract $x$ from both sides: $5x - 2 = -7$
Add 2 to both sides: $5x = -5$
Divide by 5: $x = -1$

Step3: Find y-value

Substitute $x=-1$ into $y=3x-1$:
$y = 3(-1) - 1 = -3 - 1 = -4$

Answer:

The solution is $x=-1$, $y=-4$, or the point $(-1, -4)$