Solve the following system of equations
#2x−y=−1#
#2x+y=−3#
One way to solve this system is by #"elimination"#.
The advantage of eliminating one of the unknowns is that you will then have an equation in a single unknown, which is what you solve.
Notice that you can predict that #y# will be a negative number because when you ADD it to #2x#, the amount becomes even more negative
1) Add the equations to eliminate the #y# term, which will go to zero.
#color(white)(.....)##2x −y =−1#
#+# #2x +y =−3#
———————————
#color(white)(.....)##4x##color(white)(.........)##=- 4#
#color(white)(......................)— — — — — — #
2) Now that you have an equation with only one unknown (which is #x#), you can go ahead and solve for it.
#4x = - 4#
Divide both sides by #4# to isolate #x#
#x = - 1# #larr# answer for #x#
#color(white)(......................)— — — — — — #
3) Now use the answer for #x# to solve for #y#
Sub in #-1# in the place of #x# in one of the equations and solve for #y#
#2 ( x ) −y =−1#
#2 (-1) - y = -1#
1) Clear the parentheses by distributing the #2#
#- 2 - y = - 1#
2) Add #2# to both sides to isolate the #-y# term
#- y = 1#
3) Clear the minus sign to isolate #y# by multiplying all the terms on both sides by #-1#
#y = - 1# #larr# answer for #y#
#color(white)(......................)— — — — — — #
Answer:
#x = - 1#
#y = - 1#
#color(white)(......................)— — — — — — #
Check
Sub in the values in the place of #x# and #y# in the original equations to see if they hold true.
#2 x − y = −1#
#2(-1) - (-1) "should equal" - 1#
Clear the parentheses by distributing the #2# and the minus sign
#- 2 + 1# should equal #-1#
Combine the signed numbers
#- 1# does equal #-1#
#Check!#
