Question

The system Px + Qy=R Tx + Uy=V has the solution (2,9), where P,Q,R,T,U and V does not equal 0. Select all systems of equations that have the same solution.

Answer 1

Options:

a.

`Px + Qy = R\\(P + T)x + (Q + U)y = R + V`

b.

`Px + Qy = R\\(P +2T)x +Q + 2U)y = R- 2V`

c.

`(T - P)x - (U - Q)y = V - R\\Tx + Uy = V`

d

`(T - P)x +(Q + U)y = V - R\\Tx + Uy = V`

Answer:

a.

`Px + Qy = R\\(P + T)x + (Q + U)y = R + V`

c.

`(T - P)x - (U - Q)y = V - R\\Tx + Uy = V`

Explanation:

Given

`Px + Qy = R` --- (1)

`Tx + Uy = V` --- (2)

`Solution = (2,9)`

Required

Select equations with same solution

Add equation (1) to (2)

`Px + Qy = R` --- (1)

`Tx + Uy = V` --- (2)

_________________

`Px + Tx + Qy + Uy = R + V`

Factorize:

`(P + T)x + (Q + U)y = R + V` --- (3)

So, a system of (1) and (3) can be represented as:

`Px + Qy = R\\(P + T)x + (Q + U)y = R + V`

This means (a) has the same solution.

Another possible solution is as follows:

Subtract equation (1) from (2)

`Tx + Uy = V` --- (2)

`Px + Qy = R` --- (1)

_________________

`Tx - Px + Uy - Qy = V - R`

Factorize

`(T - P)x + (U - Q)y = V - R` --- (4)

So, a system of (2) and (4) can be represented as:

`(T - P)x - (U - Q)y = V - R\\Tx + Uy = V`

This means (c) has the same solution.

Options (a) and (c) have the same solution.