SOLUTION: 1. 18-3y=5 2. -14+9a=38 3. 14r+8=32 4. 37-58b=204

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 1. 18-3y=5 2. -14+9a=38 3. 14r+8=32 4. 37-58b=204      Log On


   

Question 21988: 1. 18-3y=5

2. -14+9a=38

3. 14r+8=32

4. 37-58b=204
Found 2 solutions by Earlsdon, Alwayscheerful:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The principal idea here is to isolate the variable to one side of the equation.
This is done by "undoing" (doing the opposite operation on) whatever has been done to the variable.
1) 18 - 3y = 5 Isolate the y-term by subtracting 18 from both sides of the equation.
-3y = 5-18
-3y = -13 Now divide both sides by -3
y = 13/3
y = 4 1/3
2) -14+9a = 38 Add 14 to both sides to isolate the a-term.
9a = 38+14
9a = 52 Now divide both sides by 9.
a = 52/9
a = 5 7/9
3) 14r+8 = 32 Subtract 8 from both sides.
14r = 24 Now divide both sides by 14.
r = 24/14
r = 1 5/7
4) 37-58b = 204 Subtract 37 from both sides.
-58b = 167 Now divide by -58.
b = -(167/58)
b = -2 51/58

Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=4.33333333333333.
  • Graphical form: Equation 18-3y=5 was fully solved.
  • Text form: 18-3y=5 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+18-3y=5+%29
    For tutors: simplify_cartoon( 18-3y=5 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+18+%29-3%2Ay=5.
Moved 18 to the right of expression
It becomes -3%2Ay%2Bhighlight_green%28+18+%29=5.
Look at -3%2Ay%2B18=highlight_red%28+5+%29.
Moved these terms to the left highlight_green%28+-5+%29
It becomes -3%2Ay%2B18-highlight_green%28+5+%29=0.
Look at -3%2Ay%2Bhighlight_red%28+18+%29-highlight_red%28+5+%29=0.
Added fractions or integers together
It becomes -3%2Ay%2Bhighlight_green%28+13+%29=0.
Look at highlight_red%28+-3%2Ay%2B13+%29=0.
Solved linear equation highlight_red%28+-3%2Ay%2B13=0+%29 equivalent to -3*y+13 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=4.33333333333333.

Universal Simplifier and Solver


Done!

In fraction form: 13%2F3
2.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: a=5.77777777777778.
  • Graphical form: Equation -14%2B9a=38 was fully solved.
  • Text form: -14+9a=38 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-14%2B9a=38+%29
    For tutors: simplify_cartoon( -14+9a=38 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+14+%29%2B9%2Aa=38.
Moved -14 to the right of expression
It becomes 9%2Aa-highlight_green%28+14+%29=38.
Look at 9%2Aa-14=highlight_red%28+38+%29.
Moved these terms to the left highlight_green%28+-38+%29
It becomes 9%2Aa-14-highlight_green%28+38+%29=0.
Look at 9%2Aa-highlight_red%28+14+%29-highlight_red%28+38+%29=0.
Added fractions or integers together
It becomes 9%2Aa%2Bhighlight_green%28+-52+%29=0.
Look at 9%2Aa%2Bhighlight_red%28+-52+%29=0.
Removed extra sign in front of -52
It becomes 9%2Aa-highlight_green%28+52+%29=0.
Look at highlight_red%28+9%2Aa-52+%29=0.
Solved linear equation highlight_red%28+9%2Aa-52=0+%29 equivalent to 9*a-52 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=5.77777777777778.

Universal Simplifier and Solver


Done!

In fraction form: 52%2F9
3.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: r=1.71428571428571.
  • Graphical form: Equation 14r%2B8=32 was fully solved.
  • Text form: 14r+8=32 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+14r%2B8=32+%29
    For tutors: simplify_cartoon( 14r+8=32 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 14%2Ar%2B8=highlight_red%28+32+%29.
Moved these terms to the left highlight_green%28+-32+%29
It becomes 14%2Ar%2B8-highlight_green%28+32+%29=0.
Look at 14%2Ar%2Bhighlight_red%28+8+%29-highlight_red%28+32+%29=0.
Added fractions or integers together
It becomes 14%2Ar%2Bhighlight_green%28+-24+%29=0.
Look at 14%2Ar%2Bhighlight_red%28+-24+%29=0.
Removed extra sign in front of -24
It becomes 14%2Ar-highlight_green%28+24+%29=0.
Look at highlight_red%28+14%2Ar-24+%29=0.
Solved linear equation highlight_red%28+14%2Ar-24=0+%29 equivalent to 14*r-24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: r=1.71428571428571.

Universal Simplifier and Solver


Done!

In fraction form: 12%2F7
4.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: b=-2.87931034482759.
  • Graphical form: Equation 37-58b=204 was fully solved.
  • Text form: 37-58b=204 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+37-58b=204+%29
    For tutors: simplify_cartoon( 37-58b=204 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+37+%29-58%2Ab=204.
Moved 37 to the right of expression
It becomes -58%2Ab%2Bhighlight_green%28+37+%29=204.
Look at -58%2Ab%2B37=highlight_red%28+204+%29.
Moved these terms to the left highlight_green%28+-204+%29
It becomes -58%2Ab%2B37-highlight_green%28+204+%29=0.
Look at -58%2Ab%2Bhighlight_red%28+37+%29-highlight_red%28+204+%29=0.
Added fractions or integers together
It becomes -58%2Ab%2Bhighlight_green%28+-167+%29=0.
Look at -58%2Ab%2Bhighlight_red%28+-167+%29=0.
Removed extra sign in front of -167
It becomes -58%2Ab-highlight_green%28+167+%29=0.
Look at highlight_red%28+-58%2Ab-167+%29=0.
Solved linear equation highlight_red%28+-58%2Ab-167=0+%29 equivalent to -58*b-167 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: b=-2.87931034482759.

Universal Simplifier and Solver


Done!

In fraction form: -%28167%2F58%29
Hope this helps!