Questions on Algebra: Systems of Linear Equations answered by real tutors!

Algebra ->  Algebra -> Questions on Algebra: Systems of Linear Equations answered by real tutors!     (Log On)
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!


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
: 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.
Answer by Mathtut(1339) 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(a=5)
:
to find b just plug a's value into either equation
:
5-b=52--->subtract 5 from each side and divide by -1highlight(b=-47)
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
: 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.
Answer by jim_thompson5910(9921) About Me  (Show Source):
You can put this solution on YOUR website!
"sum of a certain number and a second number is -42" ----> x+y=-42


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




So we have the system of equations:

system(x+y=-42,x-y=52)


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


(x+y)+(x-1y)=(-42)+(52)


(1x+1x)+(1y+-1y)=-42+52 Group like terms.


2x+0y=10 Combine like terms. Notice how the y terms cancel out.


2x=10 Simplify.


x=(10)/(2) Divide both sides by 2 to isolate x.


x=5 Reduce.


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


x+y=-42 Now go back to the first equation.


5+y=-42 Plug in x=5.


5+y=-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.