Step 1) Solve each equation for #4p#:
Equation 1:
#2p + 3q = 1#
#2p + 3q - color(red)(3q) = 1 - color(red)(3q)#
#2p + 0 = 1 - 3q#
#2p = 1 - 3q#
#color(red)(2) xx 2p = color(red)(2)(1 - 3q)#
#4p = (color(red)(2) xx 1) - (color(red)(2) xx 3q)#
#4p = 2 - 6q#
Equation 2:
#4p - 5q = 13#
#4p - 5q + color(red)(5q) = 13 + color(red)(5q)#
#4p - 0 = 13 + 5q#
#4p = 13 + 5q#
Step 2) Because the left side of each equation is #4p# we can equate the right side of each equation and solve for #x#:
#2 - 6q = 13 + 5q#
#-color(blue)(13) + 2 - 6q + color(red)(6q) = -color(blue)(13) + 13 + 5q + color(red)(6q)#
#-11 - 0 = 0 + (5 + color(red)(6))q#
#-11 = 11q#
#(-11)/color(red)(11) = (11q)/color(red)(11)#
#-1 = (color(red)(cancel(color(black)(11)))q)/cancel(color(red)(11))#
#-1 = q#
#q = -1#
*Step 3) Substitute #-1# for #q# in the solution to either equation in Step 1 and calculate #p#:
#4p = 2 - 6q# becomes:
#4p = 2 - (6 * -1)#
#4p = 2 - (-6)#
#4p = 2 + 6#
#4p = 8#
#(4p)/color(red)(4) = 8/color(red)(4)#
#(color(red)(cancel(color(black)(4)))p)/cancel(color(red)(4)) = 2#
#p = 2#
The Solution Is: #p = 2# and #q = -1#