Answer:
The correct option is C. [tex]3x-3=3[/tex]
Step-by-step explanation:
To find the solution of the system of equations represented by the graph we first need to find the equations of both lines.
All horizontal line which intersects the y-axis at the point [tex](0,a)[/tex] can be written as [tex]y=a[/tex]. Therefore, the horizontal line in the graph intersects the y-axis at the point [tex](0,3)[/tex]. Its equation is [tex]y=3[/tex] (I)
For the second line, all line which intersects the x-axis at the point [tex](b,0)[/tex] and the y-axis at the point [tex](0,c)[/tex] can be written as :
[tex]\frac{x}{b}+\frac{y}{c}=1[/tex]
In the graph, the line intersects the x-axis at [tex](1,0)[/tex] and the y-axis at [tex](0,-3)[/tex] so we can write it as :
[tex]\frac{x}{1}+\frac{y}{-3}=1[/tex] ⇒ If we multiply the equation by -3 ⇒ [tex]-3x+y=-3[/tex] (II)
With (I) and (II) we are going to make a one-variable linear equation :
[tex]\left \{ {{y=3} \atop {-3x+y=-3}} \right.[/tex]
If we replace the equation (I) in equation (II) :
[tex]-3x+3=-3[/tex] (III)
If we multiply (III) by -1 ⇒
[tex]3x-3=3[/tex] (III)'
(III)' is the one-variable linear equation that can be used to find the solution of the system of equations represented by the graph. Finally, the correct option is C. [tex]3x-3=3[/tex]
