Answer:
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.
