Question

HURRY PLEASE! I BEG ITS FOR POINTS

Answer 1

Answer:

1 and 3

Step-by-step explanation:

Given the system of two equations

$\left\{\begin{array}{l}Px+Qy=R\\ \\Tx+Uy=V\end{array}\right.$

When you add, subtract, multiply the equations of the system, you get equivalent system of equations (with the same solution).

1. Add these two equations to get the system

$\left\{\begin{array}{l}Px+Qy=R\\ \\Px+Tx+QY+Uy=R+V\end{array}\right.\Rightarrow \left\{\begin{array}{l}Px+Qy=R\\ \\(P+T)x+(Q+U)y=R+V\end{array}\right.$

Hence, option 1 is correct.

2. Multiply the second equation by 2 and add two equations:

$\left\{\begin{array}{l}Px+Qy=R\\ \\2Tx+2Uy=2V\end{array}\right.\Rightarrow \left\{\begin{array}{l}Px+Qy=R\\ \\(P+2T)x+(Q+2U)y=R+2V\end{array}\right.$

Since $R+2V\neq R-2V,$ this option is false

3. Subtract two equations:

$\left\{\begin{array}{l}Tx-Px+Uy-Qy=V-R\\ \\Tx+Uy=V\end{array}\right.\Rightarrow \left\{\begin{array}{l}(T-P)x+(U-Q)y=V-R\\ \\Tx+Uy=V\end{array}\right.$

Option 3 is correct.

4. Since $U-Q\neq Q+U$, option 4 is false

5. Multiply the second equation by 5 and subtract the first equation:

$\left\{\begin{array}{l}Px+Qy=R\\ \\5Tx+5Uy=5V\end{array}\right.\Rightarrow \left\{\begin{array}{l}(5T-P)x+(5U-Q)y=5V-R\\ \\Tx+Uy=V\end{array}\right.$

Since $V-5R\neq 5V-R$, this option is false.