Solve a system of linear equations by the addition method?

2x - y = 3 (1)
3x + 4y = -1 (2)

<=> operation : 4 * (1)

8x - 4y = 12 (1')
3x + 4y = -1 (2')

<=> operation : (1') + (2')

11x = 11

<=>

x = 1 and y = 2 * 1 - 3 = -1


Answer :

x = 1 and y = -1

the first element is to eliminate between the variables the following: upload equations a million and 2 to get 4x + 4y = 4 ==> x + y = a million ==> x = a million - y then equations a million and three 3x + 5y =7 now replace for x with the previous equation 3 - 3y + 5y = 7 ==> 2y = 4 ==> y = 2 and therefore x = -a million positioned those values for x and y into between the unique equations -a million + 6 + z = 6 ==> z = a million attempt in between the others: -3 + 2 - a million = -2 or -2 + 4 - a million = a million and also you realize you've the right solutions: x = -a million y = 2 z = a million

y=2x-3 ->2x-y=3......(1)
3x+4y=-1...............(2)

(1)*3--->6x-3y=9.........(3)
(2)*2---->6x+8y=-2..........(4)

(4)-(3)----->11y=-11
y= - 1
x= 1

Method 1
2x - y = 3
3x + 4y = - 1

8x - 4y = 12
3x + 4y = - 1------ADD

11x = 11
x = 1

y = 2 - 3
y = - 1

x = 1 , y = - 1

Method 2
3x + 8x - 12 = - 1
11x = 11
x = 1

y = 2 - 3
y = - 1

x = 1 , y = - 1

y = 2x - 3
3x + 4y = -1

y = 2x - 3
y - 2x = -3
-2x + y = -3
-4(-2x + y) = -4(-3)
8x - 4y = 12

...3x + 4y = -1
+) 8x - 4y = 12 (addition)
----------------------------
11x = 11

11x = 11
x = 11/11
x = 1

y = 2x - 3
y = 2(1) - 3
y = 2 - 3
y = -1

∴ x = 1 , y = -1