SOLUTION: HELP 1. Substitution Method: 7x + 3y = -9 -6y + y =22 Find the solution? 2. Solve and Graph 2x -14 _< -7 or x -4 _> 1 Solution is {x/x _< ? or x _> ?}

Algebra ->  Finance -> SOLUTION: HELP 1. Substitution Method: 7x + 3y = -9 -6y + y =22 Find the solution? 2. Solve and Graph 2x -14 _< -7 or x -4 _> 1 Solution is {x/x _< ? or x _> ?}       Log On


   

Question 147586: HELP
1.
Substitution Method:
7x + 3y = -9
-6y + y =22
Find the solution?
2.
Solve and Graph
2x -14 _< -7 or x -4 _> 1
Solution is {x/x _< ? or x _> ?}
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
1. Substitution Method:
7x+%2B+3y+=+-9-6y+%2B+y+=22.

-First combine like terms on the right side. You end up with -5y=22. Then divide by -5 on both sides and get y=-22%2F5. Then since you have y, plug it in to the first equation and get 7x-3%28-22%2F5%29=-9. Then multiply -3 by -22/5. And get 66%2F5. Then it looks like this 7x-66%2F5=-9. Then add 66/5 to both sides and get 7x=21. Then divide both sides by seven and get x=3. So y=-22/5 and x=3.


2. Solve and Graph
2x -14 _< -7 or x -4 _> 1
Solution is {x/x _< ? or x _> ?}

2x+-14%3C=+-7 divide both sides by 2 and get x-7%3C=-7%2F2. Then subtract seven and get x%3C=7%2F2. x+-4+%3E=+1 add four to both sides x%3E=5. Graph them both as x=7/2 and x=5 first.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 3.5. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite

graph%28+500%2C+500%2C+3.5-5%2C+3.5%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A3.5+%29+

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 5. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite

graph%28+500%2C+500%2C+5-5%2C+5%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A5+%29+


Then since it is x%3C=7%2F2, shade every part of that graph to the left of x=7/2. Then since it is x%3E=5, shade every part of that graph to the right of x=5. Then you are done solving and graphing.
If you still need help graphing inequalities, check out my lesson:
http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson