How do I solve this problem using the method of elimination? x + y = 50 20x +10y = 550 Can you please show the steps as well?

1) x + y = 50
2) 20x + 10y = 550
Since both variable have the same sign in both equations the method is addition of opposite signs
In order to eliminate one variable you need the same amount
1) X -20
-20x - 20y = -1000
20x + 10y = 550
-10y = -450
y = 45
Substitute y = 45 in equation 1
x +y = 50
x = 45 = 50
x = 5
Verify
x + y = 50
LS
5 + 45 = 50
RS
50
LS = RS
the roots of the equation are 5, 45

x+y=50--1
and
20+10y=550
Taking out 10 common from both sides
2x+y=55--2

now solving 1 and 2 by elimination method

x+y=50
2x+y=55
subtracting the equations
-x=-5
x=5 put this in equation 1

5+y=50
y= 45

x+y=50
So
10x+10y=500
(10x+10y=500)-(20x+10y=550)
10x=50
x=5
x+y=50
5+y=50
y=45

x + y = 50
20x + 10y = 550
10x + 10y = 500
x = 5
y = 45

x + y = 50
2x + y = 55

x = 5
y = 45