Question

problems 3-5
use the lines in the graph to decide whether each statement is true or false.
the solution to the equation $-2x + 1 = 3x - 9$ is $x = 2$.
true false
the point $(2, -3)$ is a solution to this system of equations:
$y = -2x + 1$
$x = 2$
true false
the point $(0, 1)$ is a solution to the equation $y = -2x + 1$.
true false

Explanation:

Step1: Verify first statement

Substitute $x=2$ into $-2x+1=3x-9$:
Left side: $-2(2)+1=-4+1=-3$
Right side: $3(2)-9=6-9=-3$
Both sides are equal, and the graph shows intersection at $x=2$.

Step2: Verify second statement

Substitute $(2,-3)$ into $y=-2x+1$:
$-2(2)+1=-3$, which matches $y=-3$. $x=2$ matches the x-coordinate.

Step3: Verify third statement

Substitute $(0,1)$ into $y=-2x+1$:
$-2(0)+1=0+1=1$, which matches $y=1$.

Answer:

1. True
2. True
3. True