Step 1) Solve each equation for #6x#:
-Equation 1:
#-3x + 7y = -9#
#-3x + 7y - color(red)(7y) = -9 - color(red)(7y)#
#-3x + 0 = -9 - 7y#
#-3x = -9 - 7y#
#color(red)(-2) xx -3x = color(red)(-2)(-9 - 7y)#
#6x = (color(red)(-2) xx -9) + (color(red)(-2) xx -7y)#
#6x = 18 + 14y#
-Equation 2:
#-2x + 10y = 10#
#-2x + 10y - color(red)(10y) = 10 - color(red)(10y)#
#-2x + 0 = 10 - 10y#
#-2x = 10 - 10y#
#color(red)(-3) xx -2x = color(red)(-3)(10 - 10y)#
#6x = (color(red)(-3) xx 10) + (color(red)(-3) xx -10y)#
#6x = -30 + 30y#
Step 2) Because the left side of both equations are equal we can equate the right side of each equation and solve for #y#:
#18 + 14y = -30 + 30y#
#18 + color(red)(30) + 14y - color(red)(14y) = -30 + color(red)(30) + 30y - color(red)(14y)#
#48 + 0 = 0 + 16y#
#48 = 16y#
#48/color(red)(16) = (16y)/color(red)(16)#
#3 = (color(red)(cancel(color(black)(16)))y)/cancel(color(red)(16))#
#3 = y#
#y = 3#
Step 3) Substitute #3# for #y# into either of the equations in Step 1 and solve for #x#:
#6x = -30 + 30y# becomes:
#6x = -30 + (30 xx 3)#
#6x = -30 + 90#
#6x = 60#
#(6x)/color(red)(6) = 60/color(red)(6)#
#(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 10#
#x = 10#
The Solution Is:
#x = 10# and #y = 3#
Or
#(10, 3)#
