Question

1. $4x - y = -1$

$-x + y = x - 5$

Explanation:

Step1: Rewrite equations to slope-intercept form

First equation: $4x - y = -1$ rearranges to $y = 4x + 1$
Second equation: $-x + y = x - 5$ rearranges to $y = 2x - 5$

Step2: Find intersection via substitution

Set $4x + 1 = 2x - 5$
$4x - 2x = -5 - 1$
$2x = -6$
$x = -3$

Step3: Solve for y using x=-3

Substitute $x=-3$ into $y = 4x + 1$
$y = 4(-3) + 1 = -12 + 1 = -11$

Step4: Identify graph points (for plotting)

For $y=4x+1$:

• When $x=0$, $y=1$; when $x=1$, $y=5$

For $y=2x-5$:

• When $x=0$, $y=-5$; when $x=3$, $y=1$

Answer:

The solution to the system is $(-3, -11)$.
To plot:

1. For $y=4x+1$: plot points $(0,1)$ and $(1,5)$, draw a line through them.
2. For $y=2x-5$: plot points $(0,-5)$ and $(3,1)$, draw a line through them.
3. The lines intersect at $(-3, -11)$.