Solve the system by addition.?

Question

–2x + 5y = –19
x – 3y = 10

Answer 1

–2x + 5y = –19.....(1)
x – 3y = 10.....(2)

Multiply both sides of (2) by 2
x – 3y = 10
2(x – 3y) = 2*10
2x - 6y = 20.....(3)

Now add (1) and (3)
2x - 2x + 5y - 6y = -19 + 20
-y = 1
y = -1.....(4)

Substitute (4) in any equations. I choose (2)
x – 3y = 10
x - 3(-1) = 10
x + 3 = 10
x = 7

x = 7, y = -1 is the solution

Answer 2

x-3y=10
+3y . +3y
x=10+3y

-2(10+3y) +5y=-19
-20-6y+5y=-19
+20 . . . . .+20
-6y+5y=1
-y=1
y=-1

x-3(-1)=10
x+3=10
+-3 . +-3
x=7

-2(7)+5(-1)=-19
-14+-5=-19
-19=-19

y=-1 and x=7
Only added to both sides of equations.

Answer 3

add both equations
-2x +5y = -19
+ x -3y = 10
--------------------
-x + 2y = -9
therefore, x = 2y +9
then you plug x into one of the equations
second equation = (2y+9) - 3y = 10
-y+9 = 10
-y = 1
y = -1
then you plug y into x=2y+9 to get x
x = 2(-1) + 9
x = 7
check your answers by plugging both x and y into the two original equations
x = 7 y = -1

-2(7) + 5(-1) = -19
-19 = -19

7 - 3(-1) = 10
10 = 10

Answer 4

multiply the second equation by 2 and add the two equations
-2x+5y=-19
2x-6y=20
add them
-y=1
y=-1
substitute y with -1 in any equation
lets take the second one:
x-3(-1)=10
x+3=10
x=7

Answer 5

Multiply the second equation by 2
Add the two equations
Get y= -1
Substitute -1 for y in first equation
Get x = 7

Answer 6

-2x+5y= -19..........eq(i)

x-3y=10.................eq(ii)*2

2x-6y=20..................eq(iii)


Adding eq(i) to eq(iii),

-2x+5y= -19
2x-6y=20

we get,

-y=1
or, y= -1

putting the value of y in eq(ii), we get

x-3(-1)=10
x+3=10
x=10-3
x=7

Therefore, x=7 and y= -1