Check which of the following are solutions of the equation 2x−y=6 and which are not: (i) (3,0) (ii) (0,6) (iii) (2,−2) (iv) (√3,0) (v) (12, −5)
Equation is 2x - y = 6
(i) ( 3,0) i.e. x = 3, y = 0
Substituting the value of x and y in the equation
2×3−0=6⇒6−0=6
6 = 6 which is true.
∴ (3,0) is the solution.
(ii) (0, 6) i.e. x = 0, y = 6
Substituting the value of x and y in the equation
2×0−6=6⇒ 0−6=6
⇒ −6=6 which is not true.
∴ (0,6) is not its solution.
(iii) (2, -2) i.e. x = 2, y = -2
Substituting the value of x and y in the equation
2×2−(−2)=6⇒ 4+2=6
⇒6=6 which is true.
∴ (2,−2) is the solution.
(iv) (√3,0) i.e.x=√3, y=0
Substituting the value of x and y in the equation
2×√3−(0)=6⇒ 2√3−0=6
⇒ 2√3=6 which is not true.
∴ (√3,0) is not the solution.
(v) (12,−5) i.e. x=12,y=−5
Substituting the value of x and y in the equations.
2×12−(−5)=6⇒ 1+5=6
⇒ 6=6 which is true.
∴ (12,−5) is the solution.