Question

1. solve the system of equations by graphing.

y = 6
y = 3x - 3

1. solve t

y = -x +
3x + 3y

Explanation:

Step1: Graph $y=6$

This is a horizontal line passing through the point $(0, 6)$ (and all points where the y-value is 6).

Step2: Graph $y=3x-3$

First, identify the y-intercept: when $x=0$, $y=3(0)-3=-3$, so the point is $(0, -3)$.
Then find the x-intercept: set $y=0$, solve $0=3x-3$
$3x=3$
$x=1$, so the point is $(1, 0)$. Plot these two points and draw the line through them.

Step3: Find intersection point

The lines $y=6$ and $y=3x-3$ intersect where $6=3x-3$. Solve for $x$:
$3x=6+3$
$3x=9$
$x=3$
So the intersection point is $(3, 6)$.

Answer:

The solution to the system is $(3, 6)$