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

The prove in the procedure

Step-by-step explanation:

we have

2x+y=5 > equation 1

x-2y=-5 > equation 2

so

Replace the first equation with the sum of the equation and a multiple of the other

Multiply equation 2 by 3 both sides

3*(x-2y)=-5*3

3x-6y=-15 > equation 3

Adds equation 3 and equation 1

3x-6y=-15

2x+y=5

3x+2x-6y+y=-15+5

5x-5y=-10 > equation 4

The new system is

5x-5y=-10 > equation 4

x-2y=-5 > equation 2

Solve the system by elimination

Multiply equation 2 by -5 both sides

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

-5x+10y=25 > equation 5

Adds equation 4 and equation 5

5x-5y=-10

-5x+10y=25

-5y+10y=-10+25

5y=15

y=3

Find the value of x

substitute the value of y in the equation 2

x-2y=-5

x-2(3)=-5

x-6=-5

x=-5+6

x=1

The solution of the new system of equations is (1,3)

therefore

The solution of the new system of equations is the same solution of the original system of equations.

what's the question?

step-by-step explanation:

there is no question.