5. If x=2-a and y = 2+a is a solution of the equation 3x - 2y +6 = 0. Find the value of a. Find two more solutions of the resultant equation.
Answers
Answer :
Given : 3x - 2y + 6 = 0
x = 2 - a
y = 2+ a
To find : value of a
Solution :
3x - 2y + 6 = 0
3 ( 2 - a ) - 2 ( 2 + a ) + 6 = 0
6 - 3a - 4 - 2a + 6 = 0
- 3a - 2a = 4 - 6 - 6
- 5a = 4 - 12
- 5a = - 8
5a = 8
a = 8/5
Answer :. a = 8/5
Answer:
a = 8/5
Two more solutions :
- x = 0 ; y = 3
- x = (-2) ; y = 0
Explanation:
1. Finding the value of 'a' .
x = 2-a & y = 2+a
Equation given : 3x - 2y + 6 = 0
On putting the values of 'x' & 'y'.
3(2-a) - 2(2+a) + 6 = 0
[ (3×2) + {3× (-a)} ] + [ {(-2)×2} + {(-2)×a} ] + 6 = 0
{6 + (-3a)} + {(-4) + (-2a)} + 6 = 0
Opening the brackets :
6 - 3a - 4 - 2a + 6 = 0
6 + 6 - 4 - 3a - 2a = 0
12 - 4 - 5a = 0
8 - 5a = 0
-5a = -8
a = -8/-5
a = 8/5 Ans.
2. Two solutions for " 3x - 2y + 6 = 0
( i ) x = 0 ; y = 3
On putting the values,
3(0) - 2(3) + 6
= 0 - 6 + 6
= (-6) + 6 = 0
L.H.S. = R.HS.
So, x = 0 ; y = 3 is a Solution.
( ii ) x = (-2) ; y = 0
On putting the values,
3(-2) - 2(0) + 6
= (-6) - 0 + 6
= (-6) + 6 = 0
L.H.S. = R.HS.
So, x = (-2) ; y = 0 is a Solution