Answer the following:
→if (-1,1) is a solution of 6x+5y-k = 0 then write any two solutions of kx+3y-8=0
→if (2,-1) is a solution of 4x+by+4=0 and ax-2y+3=0 then find value of a+b
→write 3 points passes through which the graph of x=y passes
→the line ax+by+c=0 meets y axis at which point
→the line ax+by+c=0 meets X axis at which point
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Concept Used :-
If any point is solution of any line then it must satisfy the equation of line.
If any line meet at X - axis, then Y - coordinate of point intersecting X - axis is zero.
If any line meet at Y - axis, then X - coordinate of point intersecting Y - axis is zero.
Solution :-
1) If ( -1, 1 ) is a solution of 6x+5y-k = 0 then it must be satisfying the equation.
Putting x = -1 and y = 1
6x + 5y - k = 0
6(-1) + 5(1) - k = 0
-6 + 5 - k = 0
k = -1
Now, writing any two solutions of
kx+3y-8=0
Put k = -1 in the equation
kx + 3y - 8 = 0
(-1)x + 3y - 8 = 0
3y - x = 8
Now, put any value of 'x' to get 'y'
Let us put x = 1
3y - x = 8
3y - 1 = 8
3y = 9
y = 3
So, one point is ( 1, 3 )
Let us put x = 4
3y - x = 8
3y - 4 = 8
3y = 12
y = 4
So, another point is ( 4, 4 )
( 1, 3 ) and ( 4, 4 ) are two solutions.
2) (2,-1) is a solution of 4x+by+4=0 and ax-2y+3=0
Put x = 2 and y = -1 in given equations
4x + by + 4 = 0
4(2) + b(-1) + 4 = 0
8 - b + 4 = 0
b = 12
ax - 2y + 3 = 0
a(2) - 2(-1) + 3 = 0
2a + 2 + 3 = 0
2a = -5
a = -5/2
So, a + b = 12 - 5/2 = 19/2
3) 3 points which passes through y = x
Put y = 1,2 and 3
then
x = 1,2 and 3
So, three such points are
( 1, 1 ) , ( 2, 2 ) and ( 3, 3 )
4) Line ax+by+c=0 meets Y axis, it means x = 0 for point which meet axis
Put x = 0 in equation
ax + by + c = 0
a(0) + by + c = 0
by + c = 0
y = -c/b
So, point is ( 0, -c/b )
5) Line ax+by+c=0 meets X axis, it means y = 0 for point which meet axis
Put y = 0 in equation,
ax + by + c = 0
ax + b(0) + c = 0
ax + c = 0
x = -c/a
So, point is ( -c/a, 0 )