Step 1) Solve each equation for 2p2p:
Equation 1
2p - 5q = 142p−5q=14
2p - 5q + color(red)(5q) = 14 + color(red)(5q)2p−5q+5q=14+5q
2p - 0 = 14 + 5q2p−0=14+5q
2p = 14 + 5q2p=14+5q
Equation 2
p + 3/2q = 5p+32q=5
p + 3/2q - color(red)(3/2q) = 5 - color(red)(3/2q)p+32q−32q=5−32q
p + 0 = 5 - 3/2qp+0=5−32q
p = 5 - 3/2qp=5−32q
color(red)(2) xx p = color(red)(2)(5 - 3/2q)2×p=2(5−32q)
2p = (color(red)(2) xx 5) - (color(red)(2) xx 3/2q)2p=(2×5)−(2×32q)
2p = 10 - 3q2p=10−3q
Step 2) Substitute 10 - 3q10−3q from the second equation for 2p2p in the first equation and solve for pp:
2p = 14 + 5q2p=14+5q becomes:
10 - 3q = 14 + 5q10−3q=14+5q
-color(blue)(14) + 10 - 3q + color(red)(3q) = -color(blue)(14) + 14 + 5q + color(red)(3q)−14+10−3q+3q=−14+14+5q+3q
-4 - 0 = 0 + (5 + color(red)(3))q−4−0=0+(5+3)q
-4 = 8q−4=8q
-4/color(red)(8) = (8q)/color(red)(8)−48=8q8
-1/2 = (color(red)(cancel(color(black)(8)))q)/cancel(color(red)(8))
-1/2 = q or q = -1/2
Step 3) Substitute -1/2 for q in either of the equations from Step 1 and calculate p:
2p = 14 + 5q becomes:
2p = 14 + (5 * -1/2)
2p = 14 - 5/2
2p = (2/2 * 14) - 5/2
2p = 28/2 - 5/2
2p = 23/2
color(red)(1/2) * 2p = color(red)(1/2) * 23/2
1p = 23/4
p = 23/4
The Solution Is: p = 23/4 and q = -1/2
