Question

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

A. x = 3
B. 3 – 3x = 3
C. 3x – 3 = 3
D. y = 3x

Answer 1

C looks correct

here's a tip use desmos graphing next time

Answer 2

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

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 :

`(x)/(b)+(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 :

`(x)/(1)+(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`