Question

X+y=2 x-y=4 substitution

Answer 1

We have following two given equations which are:

`\implies\sf{x + y = 2 \: ...(1)}`

`\implies\sf{x - y = 4}`

`\implies\sf{x = 4 + y \: ...(2)}`

Now replacing the value of x of equation (2) in equation (1),

`\implies\sf{x + y = 2}`

`\implies\sf{4 + y + y = 2}`

`\implies\sf{4 + 2y = 2}`

`\implies\sf{2y = 2 - 4}`

`\implies\sf{2y = - 2}`

`\implies\sf{y = ( - 2)/(2) }`

`\implies\sf{y = - 1}`

Now replacing y = -1 in equation (1),

`\implies\sf{x + y = 2}`

`\implies\sf{x + ( - 1) = 2}`

`\implies\sf{x - 1 = 2}`

`\implies\sf{x = 2 + 1}`

`\implies\sf{x = 3}`

• The values of x and y are 3 and -1

Answer 2

x = 3

y = -1

Explanation:

x + y = 2 ---------------------(I)

x -y = 4

x = 4 + y -----------------(II)

Substitute x = 4 + y in equation (I)

4 + y + y = 2

4 + 2y = 2

Subtract 4 from both sides

2y = 2 - 4

2y = - 2

Divide both sides by 2

y = -2/2

y= -1

Substitute y = -1 in equation(II)

x = 4 - 1

x = 3