SOLUTION: How to find all whole number solutions of each system using a table. {{{ x + y < 8 }}} {{{ 3x < 6 + 6 }}} Also under the '<' in the 2nd equation, there is a line under it

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: How to find all whole number solutions of each system using a table. {{{ x + y < 8 }}} {{{ 3x < 6 + 6 }}} Also under the '<' in the 2nd equation, there is a line under it      Log On


   

Question 362094: How to find all whole number solutions of each system using a table.
+x+%2B+y+%3C+8+
+3x+%3C+6+%2B+6+
Also under the '<' in the 2nd equation, there is a line under it, symbolizing that it is an inequality.
Answer by HasanSahin(52) About Me  (Show Source):
You can put this solution on YOUR website!
First system : x+y<8 and
Second System : x<=4 if you want to solve these systems separately.
First think that x+y = 8 and plot this such that;
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+1+y+=+8 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/1 = 8.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/1 = 8.
  • Slope is -1/1 = -1.
  • Equation in slope-intercept form: y=-1*x+8.
graph%28+500%2C+500%2C+8-8%2C+8%2B8%2C+8-8%2C+8%2B8%2C+-1%2Ax%2B8+%29+


After then you will see that the original equation is x + y < 8 so that you have to modify your line like a discontinuous line(not ____ like _ _ _) and rake the below part of the line because you want the smaller values rather than 8. I hope I could explain it in here because I can not draw it..
The second system is also in same logic.. think like x =4 and plot it
After then you will see that the original equation is x<= 4 so that at this time you do not have to modify your line because it includes 4 and rake the left part of the line because you want the smaller and equal values rather than 4.
RF.