Step 1) Solve each equation for #4p#:
Equation 1:
#2p + 3q = 10#
#2p + 3q - color(red)(3q) = 10 - color(red)(3q)#
#2p + 0 = 10 - 3q#
#2p = 10 - 3q#
#color(red)(2) * 2p = color(red)(2)(10 - 3q)#
#4p = (color(red)(2) * 10) - (color(red)(2) * 3q)#
#4p = 20 - 6q#
Equation 2:
#2q - 4p = 44#
#-color(blue)(44) + 2q - 4p + color(red)(4p) = -color(blue)(44) + 44 + color(red)(4p)#
#-44 + 2q - 0 = 0 + 4p#
#-44 + 2q = 4p#
#4p = -44 + 2q#
Step 2) Because the left side of each equation is #4p# we can equate the right side of each equation and solve for #q#:
#20 - 6q = -44 + 2q#
#color(red)(44) + 20 - 6q + color(red)(6q) = color(red)(44) - 44 + 2q + color(red)(6q)#
#64 - 0 = 0 + (2 + color(red)(6))q#
#64 = 8q#
#64/color(red)(8) = (8q)/color(red)(8)#
#8 = (color(red)(cancel(color(black)(8)))q)/cancel(color(red)(8))#
#8 = q#
#q = 8#
*Step 3) Substitute #8# for #q# in the solution to either equation in Step 1 and calculate #p#:
#4p = 20 - 6q# becomes:
#4p = 20 - (6 * 8)#
#4p = 20 - 48#
#4p = -28#
#(4p)/color(red)(4) = -28/color(red)(4)#
#(color(red)(cancel(color(black)(4)))p)/cancel(color(red)(4)) = -7#
#p = -7#
The Solution Is: #p = -7# and #q = 8#
