Question

Which one-variable linear equation can be used to find the solution of the system of equations represented by this graph?

Answer 1

C looks correct

here's a tip use desmos graphing next time

Answer 2

Answer:

The correct option is C. $3x-3=3$

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 $(0,a)$ can be written as $y=a$. Therefore, the horizontal line in the graph intersects the y-axis at the point $(0,3)$. Its equation is $y=3$ (I)

For the second line, all line which intersects the x-axis at the point $(b,0)$ and the y-axis at the point $(0,c)$ can be written as :

$\frac{x}{b}+\frac{y}{c}=1$

In the graph, the line intersects the x-axis at $(1,0)$ and the y-axis at $(0,-3)$ so we can write it as :

$\frac{x}{1}+\frac{y}{-3}=1$ ⇒ If we multiply the equation by -3 ⇒ $-3x+y=-3$ (II)

With (I) and (II) we are going to make a one-variable linear equation :

$\left \{ {{y=3} \atop {-3x+y=-3}} \right.$

If we replace the equation (I) in equation (II) :

$-3x+3=-3$ (III)

If we multiply (III) by -1 ⇒

$3x-3=3$ (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. $3x-3=3$