Question 581429
5x +  y = 18
6x + 7y = -19
to graph this we want the equations in the slope intercept form; y = mx + b
We will graph each equation separately, then together
y = -5x + 18
We need at least two points to graph a linear equation, substitute for x and find y, A table
:
 x | y
-------
-2 |28; (y = -5(-2) + 18; y = +10 + 18)
 0 |18
+2 | 8
:
The graph looks like this
{{{ graph( 300, 200, -6, 10, -20, 30, -5x+18) }}}
:
Do the same with the 2nd equation
6x +7y = -19
7y = -6x - 19
y = {{{-6/7}}}x - {{{19/7}}}
:
x | y
-------
-2 |-1; 
 0 |-19
+5 |-7
:
The graph looks like this
{{{ graph( 300, 200, -6, 10, -20, 30, (-6/7)x-(19/7)) }}}
:
Together:
{{{ graph( 300, 200, -6, 10, -20, 30, -5x+18, (-6/7)x-(19/7)) }}}
Where the two graphs intersect x=5, y=-7 is the solution to this system
And it is the only solutions so it "consistent" 
and
in this system x = the independent variable and y is the dependent
:
Another words the value of y is dependent on the value of x
;
Note that you can confirm this if you substitute 5 for x and -7 for y in both original equations, you find the equations are true, for this solution