SOLUTION: Please help me solve this equation: using a system of two equations. The sum of a certain number and a second number is -42. The first number minus the second is 52. Find t

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Please help me solve this equation: using a system of two equations. The sum of a certain number and a second number is -42. The first number minus the second is 52. Find t      Log On


   

Question 168849This question is from textbook Prentice Hall Algebra 2 with trigonometry
: Please help me solve this equation:
using a system of two equations.

The sum of a certain number and a second number is -42. The first number minus the second is 52. Find the numbers. This question is from textbook Prentice Hall Algebra 2 with trigonometry

Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the numbers a and b
:
a+b=-42...eq 1
a-b=52....eq 2
using the elimination method to solve means we try to eliminate one of the variables and we can do that just by adding the 2 equation together(the b terms cancel out.
:
we end up with 2a=10---> divide by 2 and highlight%28a=5%29
:
to find b just plug a's value into either equation
:
5-b=52--->subtract 5 from each side and divide by -1highlight%28b=-47%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"sum of a certain number and a second number is -42" ----> x%2By=-42


"first number minus the second is 52" ----> x-y=52




So we have the system of equations:

system%28x%2By=-42%2Cx-y=52%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-1y%29=%28-42%29%2B%2852%29


%281x%2B1x%29%2B%281y%2B-1y%29=-42%2B52 Group like terms.


2x%2B0y=10 Combine like terms. Notice how the y terms cancel out.


2x=10 Simplify.


x=%2810%29%2F%282%29 Divide both sides by 2 to isolate x.


x=5 Reduce.


------------------------------------------------------------------


x%2By=-42 Now go back to the first equation.


5%2By=-42 Plug in x=5.


5%2By=-42 Multiply.


y=-42-5 Subtract 5 from both sides.


y=-47 Combine like terms on the right side.


So our answer is x=5 and y=-47.


Which form the ordered pair .


This means that the system is consistent and independent.