Question

1. $\

$$\begin{cases} y = -x + 4 \\\\ y = 2x - 5 \\end{cases}$$

$
solution:

Explanation:

Step1: Set equations equal

Since $y=-x+4$ and $y=2x-5$, set $-x+4=2x-5$.

Step2: Solve for $x$

Rearrange to isolate $x$:
$$-x-2x=-5-4$$
$$-3x=-9$$
$$x=\frac{-9}{-3}=3$$

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

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

Answer:

The solution to the system is $(3, 1)$

To graph the lines:

1. For $y=-x+4$: plot the y-intercept $(0,4)$ and use slope $-1$ to find another point (e.g., $(4,0)$), then draw the line.
2. For $y=2x-5$: plot the y-intercept $(0,-5)$ and use slope $2$ to find another point (e.g., $(3,1)$), then draw the line. The lines intersect at $(3,1)$.