Question

Which equation does the graph of the systems of equations solve?

a) -1/3x+1=-2x-4
b) 1/3x+1=-2x-4
c) 1/3x+1=2x-4
d) -1/3x-1=-2x-4

Answer 1

We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.

Explanation:

From the given graph, it is clear that the two lines meet at the point (3, 2).

In other words,

• at x =3, y = 2

Thus,

The point of intersection between two lines is:

(x, y) = (3, 2)

Here:

x = 3 is the value of the x-coordinate

y = 2 is the value of the y-coordinate

Now, checking the equation i.e. 1/3x+1=2x-4 to determine whether the equation contains the correct value of x-coordinate or not.

`(1)/(3)x+1=2x-4`

Subtract 1 from both sides

`(1)/(3)x+1-1=2x-4-1`

Simplify

`(1)/(3)x=2x-5`

subtract 2x from both sides

`(1)/(3)x-2x=2x-5-2x`

Simplify

`-(5)/(3)x=-5`

Multiply both sides by 5

`3\left(-(5)/(3)x\right)=3\left(-5\right)`

Simplify

`-5x=-15`

Divide both sides by -5

`(-5x)/(-5)=(-15)/(-5)`

Simplify

`x=3`

Therefore, the value of x = 3

Conclusion:

We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.