Question

A system of equations is created by using the line represented by 2x+4y=0 and the line represented by the data in the table below.

–1 8
3 –4
5 –10
6 –13
(not answer choices!^)

What is the x-value of the solution to the system?

Answer 1

its 2

Explanation:

Answer 2

We have been given the first equation as
`2x+4y=0`

Now, we find the second equation from the given table. From the table, we have two points
`(-1,8),(3,-4)`

The slope of the line is given by

`m=(y_2-y_1)/(x_2-x_1)\\ \\ m=(-4-8)/(3+1)\\ \\ m=(-12)/(4)\\ \\ m=-3`

Thus, the equation of the line is given by

`y-y_1=m(x-x_1)\\ y-8=-3(x+1)\\ y-8=-3x-3\\ y=-3x+5`

Therefore, we have the system of equations

`2x+4y=0...............(1)\\ y=-3x+5................(2)`

Substitute the value of y in equation 1, we get

`2x+4(-3x+5)=0\\ 2x-12x+20=0\\ -10x=-20\\ \\ x=(-20)/(-10) \\ \\ x=2`

The x value is given by 2