SOLUTION: Would someone please help me with this problem with step by step instructions? Solve the systems of equations by graphing 5x + y = 18 6x + 7y = -19 What is the solution? Is i

Algebra ->  Inequalities -> SOLUTION: Would someone please help me with this problem with step by step instructions? Solve the systems of equations by graphing 5x + y = 18 6x + 7y = -19 What is the solution? Is i      Log On


   

Question 581429: Would someone please help me with this problem with step by step instructions?
Solve the systems of equations by graphing
5x + y = 18
6x + 7y = -19
What is the solution? Is it consistent or inconsistent?
Dependent or independent?
(I do not know what that means)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+-5x%2B18%29+
:
Do the same with the 2nd equation
6x +7y = -19
7y = -6x - 19
y = -6%2F7x - 19%2F7
:
x | y
-------
-2 |-1;
0 |-19
+5 |-7
:
The graph looks like this
+graph%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+%28-6%2F7%29x-%2819%2F7%29%29+
:
Together:
+graph%28+300%2C+200%2C+-6%2C+10%2C+-20%2C+30%2C+-5x%2B18%2C+%28-6%2F7%29x-%2819%2F7%29%29+
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