Answer:
x = 3
y = -1
Step-by-step 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
We have following two given equations which are:
[tex]\implies\sf{x + y = 2 \: ...(1)}[/tex]
[tex]\implies\sf{x - y = 4}[/tex]
[tex]\implies\sf{x = 4 + y \: ...(2)}[/tex]
Now replacing the value of x of equation (2) in equation (1),
[tex]\implies\sf{x + y = 2}[/tex]
[tex]\implies\sf{4 + y + y = 2}[/tex]
[tex]\implies\sf{4 + 2y = 2}[/tex]
[tex]\implies\sf{2y = 2 - 4}[/tex]
[tex]\implies\sf{2y = - 2}[/tex]
[tex]\implies\sf{y = \frac{ - 2}{2} }[/tex]
[tex]\implies\sf{y = - 1}[/tex]
Now replacing y = -1 in equation (1),
[tex]\implies\sf{x + y = 2}[/tex]
[tex]\implies\sf{x + ( - 1) = 2}[/tex]
[tex]\implies\sf{x - 1 = 2}[/tex]
[tex]\implies\sf{x = 2 + 1}[/tex]
[tex]\implies\sf{x = 3}[/tex]
