Question

From the choice given below, choose the equation whose graphs are given in fig 4.6 and 4.7. i) y = x i) y = x + 2 ii) x + y = 0 ii) y = x – 2 iii) y = 2x iii) y = -x + 2 iv) 2 + 3y = 7x iv) x + 2y = 68​

Answer 1

Answer:

In the given fig. (i), the solutions of the equation are (−1,1),(0,0) and (1,−1).

∴ the equation which satisfies these solutions is the correct equation.

Equation (ii) x+y=0, satisfies these solutions.

Proof:

If we put the value of x=−1 and y=1 in the equation x+y=0

=x+y=−1+1=0

∴L.H.S=R.H.S

if we put the the value of x = 0 and y = 0

=x+y=0+0=0

∴L.H.S=R.H.S

If we put the value of x=1 and y=−1

=x+y=1+(−1)=1–1=0

L.H.S=R.H.S

Hence, option (ii) x+y=0 is correct.

In the given Fig.(ii) the solutions of the equation are (−1,3),(0,2) and (2,0).

∴The equation which satisfies these solutions is the correct equation.

Equation (iii) y=−x+2 , satisfies these solutions.

Proof:

If we put the value of x=−1 and y=3 in the equation y=−x+2

y=−x+2

3=−(−1)+2

3=3

∴L.H.S=R.H.S

if we put the the value of x=0 and y=2

y=−x+2

2=−0+2

2=2

∴L.H.S=R.H.S

If we put the value of x=2 and y=0

y=−x+2

0=−2+2

0=0

L.H.S=R.H.S

Hence, option (iii) y=−x+2 is correct.