Step 1) Solve both equations for #4y#:
- Equation 1:
#6x + 4y = -4#
#-color(red)(6x) + 6x + 4y = -color(red)(6x) - 4#
#0 + 4y = -6x - 4#
#4y = -6x - 4#
- Equation 2:
#3x + 4y = 2#
#-color(red)(3x) + 3x + 4y = -color(red)(3x) + 2#
#0 + 4y = -3x + 2#
#4y = -3x + 2#
Step 2) Because the right side of both equations are equal to #4y# on the left side of each equation, we can equate the right sides of each equation and solve for #x#:
#-6x - 4 = -3x + 2#
#color(red)(6x) - 6x - 4 - color(blue)(2) = color(red)(6x) - 3x + 2 - color(blue)(2)#
#0 - 6 = (color(red)(6) - 3)x + 0#
#-6 = 3x#
#-6/color(red)(3) = (3x)/color(red)(3)#
#-2 = (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))#
#-2 = x#
#x = -2#
Step 3) Substitute #-2# for #x# into the solutions for either of the original equations and solve for #y#:
#4y = -3x + 2# becomes:
#4y = (-3 * -2) + 2#
#4y = 6 + 2#
#4y = 8#
#(4y)/color(red)(4) = 8/color(red)(4)#
#(color(red)(cancel(color(black)(4)))y)/cancel(color(red)(4)) = 2#
#x = -2#
The Solution Is: #x = -2# and #x = -2# or #(-2, 2)#
