Question

17. If x=a y=b is the solutions of the system of equations x-y=2 and x+y=4, then find
the values of a and b.​

Answer 1

Answer:

value of x is 3 and y is 2.........

Answer 2

Answer:

Given, x=a and y=b.

Given equations, x-y=2( assume it as equation 1)

x+y=4( assume it as equation 2)

Equation 1+2,

x-y=2

x+y=4

- - - - - - -

2x=6( y gets cancelled as there is a negative y and a positive y implies y-y=0)

x=6/2

x=3

But x=a implies a=3

substitute a in equation 1 (it can be substituted even in equation 2)

x-y=2

3-y=2

y=3-2

y=1

But y=b implies b=1

Therefore, a=3 and b=1

or second method :-

As x=a and y=bthen

⇒a−b=2............(1)

⇒a+b=4............(2)

Adding eq1 and eq2

⇒2a=6

⇒a= 2 6  =3

Substitute the value of a in eq1

⇒3−b=2

⇒−b=2−3

⇒b=1

Hence the value of a=3  and b=1

thank you