Solve the system of equations
#−9x+7y=8#
# −6x+4y=2#
To solve for #y#, multiply all the terms of each equation so that the coefficients of #x# are the same
1) Multiply all the terms of the first equation by #-2#
After you have multiplied, you will get this:
#18x - 14y = - 16#
2) Multiply all the terms of the second equation by #+3#
After you have multiplied, you will get this:
#-18x + 12y = 6#
3) Combine the equations to let the #x# terms go to zero
#color(white)(m)##18x - 14y = - 16#
#-18x + 12y = 6#
#color(white)()#―――――――――――
#color(white)(mm)##color(lightgray)0 - 2y =-10#
4) Divide both sides by #-2# to isolate #y#
#y = 5# #larr# answer for #y#
#color(white)(mmm)#―――――――――――
To solve for #x#, sub in the value of #y#
1) Sub in #5# in the place of #y# in one of the original equations
#−9x+7 y =8#
#−9x+7(5)=8#
2) Clear the parentheses
#-9x + 35 = 8#
3) Subtract #35# from both sides to isolate the #-9x# term
#-9x = - 27#
4) Divide both sides by #-9# to isolate #x#
#x = 3# #larr# answer for #x#
#color(white)(mmm)#―――――――――――
Check
Sub the values for #x# and #y# into the original equations
#−9 x +7 y=8#
#-9(3) + 7(5)# should equal #8#
#color(white)(.)##-27 + 35# should equal #8#
#8# does equal #8# ✓
#color(white)()#―――――――――――
# −6 x +4 y=2#
#-6(3) + 4(5)# should equal #2#
#color(white)(.)##-18 + 20# should equal #2#
#2# does equal #2# ✓
#Check#
