Mr. Lee asks a student to solve the following system of linear equations. {-28=-40q-14p 10q+4=2p Which ordered pair (p, q) is a solution to the system? (-7/5,-2) (-2,-7/5) (0, 2) (2, 0)

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zrh2sfo zrh2sfo · Answer 1 · 2019-06-04T19:20:05+02:00

Answer:

p = 2 , q = 0

Step-by-step explanation:

Solve the following system:

{-28 = -14 p - 40 q | (equation 1)

10 q + 4 = 2 p | (equation 2)

Express the system in standard form:

{14 p + 40 q = 28 | (equation 1)

-(2 p) + 10 q = -4 | (equation 2)

Add 1/7 × (equation 1) to equation 2:

{14 p + 40 q = 28 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Divide equation 1 by 2:

{7 p + 20 q = 14 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Multiply equation 2 by 7/110:

{7 p + 20 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Subtract 20 × (equation 2) from equation 1:

{7 p+0 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Divide equation 1 by 7:

{p+0 q = 2 | (equation 1)

0 p+q = 0 | (equation 2)

Collect results:

Answer: {p = 2 , q = 0