Consider the following system with a solution (1,3) equation 1 of the system 2x+y=5 equation 2 of the system x-2y=-5 prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution

We rewrite the first equation:

(2) * (2x + y) = (2) * (5)

4x + 2y = 10

We now add this equation with the second equation:

(4x + 2y = 10) +

(x-2y = - 5)

>> 5x = 5

The resulting system is:

5x = 5

x-2y = - 5

Where we conclude:

x = 5/5 = 1

y = (1 + 5) / (2) = 6/2 = 3

Answer:

a system with the same solution

5x = 5

x-2y = - 5

Solutions:

x = 1

y = 3