The system Px + Qy = R has the solution (3,-1), where F, G, H, P, Q, and Fx + Gy = H R are nonzero real numbers. Sele

Question

The system Px + Qy = R has the solution (3,-1), where F, G, H, P, Q, and
Fx + Gy = H
R are nonzero real numbers.

Select all the systems that are also guaranteed to have the solution (3,-1)

a.) (P + F)x + (Q + G)Y = R + H

Fx + Gy = H

b.) (P + F)x + Qy = R + H

Fx + (G + Q)y = H

c.) Px + Qy = R

(3P + F)x + (3Q + G)y = 3H + R

d.) Px + Qy = R

(F – 2P)x +(G – 2Q)y = H – 2R

e.) Px + Qy = R

5Fx + 5Gy = 5H

*Please explain how you got your answer because I really don’t understand this!

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RobertKer 4 years 2021-07-20T06:42:33+00:00 1 Answers 176 views 0

Answers ( )

    0
    2021-07-20T06:44:25+00:00

    Answer:

    The systems that are guaranteed have the solution (3, -1) are;

    a.) (P + F)·x + (Q + G)·y = R + H

    F·x + G·y = H

    d.) P·x + Q·y = R

    (F – 2·P)·x + (G – 2·Q)·y = H – 2·R

    e) P·x + Q·y = R

    5·F·x + 5·G·y = 5·H

    Step-by-step explanation:

    The given system of equation are;

    a) P·x + Q·y = R…(1)

    F·x + G·y = H…(2)

    The solution of the system of equation = (3, -1)

    Adding equation (1) to equation (2) gives;

    P·x + Q·y + F·x + G·y = R + H

    (P + F)·x + (Q + G)·y = R + H…(3)

    Therefore, given that equation (3) is obtained from equation (1) and (2) by addition, equation (3), (P + F)·x + (Q + G)·y = R + H, we have;

    The system of  equation;

    (P + F)·x + (Q + G)·y = R + H

    F·x + G·y = H, derived from the given system of equation Is bound to have the same same solution (3, -1) as the given system of equation

    d.) By multiplying equation (1) by 2, we have;

    2 × (P·x + Q·y) = 2 × R

    2·P·x + 2·Q·y = 2·R…(4)

    Subtracting equation (4) from equation (2) gives;

    F·x + G·y – (2·P·x + 2·Q·y) = H – 2·R

    F·x – 2·P·x + G·y – 2·Q·y = H – 2·R

    (F – 2·P)·x + (G – 2·Q)·y = H – 2·R

    Therefore, for the following system, obtained from the original system, we have that the solution is (3, -1);

    P·x + Q·y = R

    (F – 2·P)·x + (G – 2·Q)·y = H – 2·R

    e) For the system of equation, we have;

    P·x + Q·y = R

    5·F·x + 5·G·y = 5·H

    The above system of equation is obtained from the original system by multiplying equation (2) by 5, therefore the solution of the system P·x + Q·y = R, 5·F·x + 5·G·y = 5·H is the same as the solution for the original system of equations (3, -1).

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