Question

the graphs of two lines are shown here. which system of equations is best represented by this graph ?A) x + y = 82x - 9y = 4 B) -x + y = 99x + 2y = 4 C) 4x + y = 6 -2x + y = -5D) x - 4y = -6-2x - y = 5

Answer 1

We have different manners to solve this problem. One of the ways is to find the equation of both lines and the other one you can just select a point and substitute on the equations to see if the value on y is correct. So let's use this second way. On the graph, we can see that in the crescent equation when x = 5, y = 5. Thus let substitute x by 5 in all the crescent equations (crescent equations have the number that follows x positive). Obs: To find these equations and evaluate the x sign you have to isolate the y. Example:

`x+y=8`
`y\text{ = -x+8}`

This is a decreasing equation (sign of x is negative). Back to exercise, let's analyze all the letters:

`2x-9y=4\text{ is a crescent equation}`

So let's see if the condition is real:

`2*5-9*5\\e4`

At letter B:

`-x+y=9\text{ is a crescent equation}`
`-5+5\\e9`

At letter C:

`-2x+y=-5\text{ is a crescent equation}`
`-2*5+5=-5\text{ !!!! That is True!}`

We also have to check letter D:

`x-4y=-6\text{ is a crescent equation}`
`5-4*5\\e-6`

Seeing all these statements above we can affirm that the only one that is true is what happens in the letter C!