Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution

Answer with Step-by-step explanation:

Consider the system of equation

.....(1)

...(2)

Now, multiply equation (1) by 2 and we get

...(3)

...(2)

Adding equation (3) with equation (2)

Then, we get

..(4)

Now, substitute in equation (2)

Equation (2) and equation (4)   intersect at point (.

Therefore, the solution of equation (2) and equation (4)

is (.

Substitute in equation (1)

Then, we get

LHS=RHS

It means ) is a solution of equation (1).

Substitute y=5 in equation (2)

Then, we get

LHS=RHS

Therefore, the point satisfied the equation (1) and equation (2).

Hence, the solution of equation (1) and equation (2) is (.

We can say that solution of equation (1) and equation (2) and equation (2) and equation (4) is same.