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:

$2\times5-9\times5\ne4$

At letter B:

$-x+y=9\text{ is a crescent equation}$$-5+5\ne9$

At letter C:

$-2x+y=-5\text{ is a crescent equation}$$-2\times5+5=-5\text{ !!!! That is True!}$

We also have to check letter D:

$x-4y=-6\text{ is a crescent equation}$$5-4\times5\ne-6$

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