Options:
a.
[tex]Px + Qy = R\\(P + T)x + (Q + U)y = R + V[/tex]
b.
[tex]Px + Qy = R\\(P +2T)x +Q + 2U)y = R- 2V[/tex]
c.
[tex](T - P)x - (U - Q)y = V - R\\Tx + Uy = V[/tex]
d
[tex](T - P)x +(Q + U)y = V - R\\Tx + Uy = V[/tex]
Answer:
a.
[tex]Px + Qy = R\\(P + T)x + (Q + U)y = R + V[/tex]
c.
[tex](T - P)x - (U - Q)y = V - R\\Tx + Uy = V[/tex]
Step-by-step explanation:
Given
[tex]Px + Qy = R[/tex] --- (1)
[tex]Tx + Uy = V[/tex] --- (2)
[tex]Solution = (2,9)[/tex]
Required
Select equations with same solution
Add equation (1) to (2)
[tex]Px + Qy = R[/tex] --- (1)
[tex]Tx + Uy = V[/tex] --- (2)
_________________
[tex]Px + Tx + Qy + Uy = R + V[/tex]
Factorize:
[tex](P + T)x + (Q + U)y = R + V[/tex] --- (3)
So, a system of (1) and (3) can be represented as:
[tex]Px + Qy = R\\(P + T)x + (Q + U)y = R + V[/tex]
This means (a) has the same solution.
Another possible solution is as follows:
Subtract equation (1) from (2)
[tex]Tx + Uy = V[/tex] --- (2)
[tex]Px + Qy = R[/tex] --- (1)
_________________
[tex]Tx - Px + Uy - Qy = V - R[/tex]
Factorize
[tex](T - P)x + (U - Q)y = V - R[/tex] --- (4)
So, a system of (2) and (4) can be represented as:
[tex](T - P)x - (U - Q)y = V - R\\Tx + Uy = V[/tex]
This means (c) has the same solution.
Options (a) and (c) have the same solution.
