Question

here is a system of equations.
\

$$\begin{cases} y = x - 4 \\\\ y = 2x - 7 \\end{cases}$$

graph the system. then write its solution. note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

Step1: Set equations equal (solve for $x$)

Since $y=y$, set $x-4=2x-7$

Step2: Isolate $x$ variable

Subtract $x$ from both sides: $-4=x-7$
Add 7 to both sides: $x=3$

Step3: Find $y$ using $x=3$

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

Step4: Verify with second equation

Substitute $x=3$ into $y=2x-7$: $y=2(3)-7=6-7=-1$ (matches)

Answer:

The solution is $(3, -1)$

(To graph: For $y=x-4$, plot y-intercept $(0,-4)$ and use slope 1 to draw the line. For $y=2x-7$, plot y-intercept $(0,-7)$ and use slope 2 to draw the line; the lines intersect at $(3, -1)$)