Write the equations in such a form that you get both of the coefficients of one of the variables to be the same.
Once you have two coefficients that are the same, you can get that variable to go to zero.
Then you will have #"one"# equation in #"one"# unknown, which you can solve easily.
#color(white)(.....................)# . . . . . . . . . .
The best solution for this set of equations is to divide all the terms on both sides of the second equation by #7# to make the coefficients smaller.
#7x−7y=−7#
1) Divide all the terms on both sides by #7# to make the coefficients smaller
#x - y = - 1#
Now you can multiply all the terms on both sides by #9# to give the #x# term the same coefficient that it has in the other equation.
2) Multiply all the terms on both sides by #9# to make the coefficients of both #x# terms the same
#9x - 9y = - 9#
Now you can subtract one equation from the other in order to make the #x# terms go to zero.
3) Subtract the equations
#color(white)(....n)##9x - 9y = - 9#
#-# #(9x−10y=− 8)#
――――――――――――
#color(white)(.................)# #y = color(white)(m)# -1#larr# answer for #y#
#color(white)(.....................)# . . . . . . . . . .
Now that you have a value for #y#, you can use it to find the value of #x#
Use one of the original equations to sub in #-1# in the place of #y#, then solve for #x#
4) Sub in #-1# for #y# and solve for #x#
#9x−10 ( y ) =−8#
#9x−10(-1)=−8#
5) Clear the parentheses by distributing the #-10#
#9x + 10 = - 8#
6) Subtract #10# from both sides to isolate the #9x# term
#9x = - 18#
7) Divide both sides by #9# to isolate #x#
#x = - 2##larr# answer for #x#
#color(white)(.....................)# . . . . . . . . . .
#"Answer"#:
#x = - 2#
#y = - 1#
#color(white)(.....................)# . . . . . . . . . .
Check
Sub in the values in the original equations and see if the equations are still true.
#7color(white)(..)x color(white)(..)−7color(white)(..)ycolor(white)(..........)=color(white)(.n..)−7#
#7(-2) −7(-1)# should equal #−7#
#-14 + 7# should equal #-7#
#-7# does equal #-7#
#Check!#
