3. What is the condition that the pair of linear equations
kx + 2y = 5 and 3r + y = 1 has a unique solution?
4. If x=0, y = b is the solution of the equations x - y = 2 and
x+y 4, then find the values of a and b.
Answers
Answer:
No solution....
Step-by-step explanation:
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What is the condition that pair of linear euqations kx+2y=5 & 3x+y=1 have unique solution?
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ANSWER
Given that equations are kx + 2y = 5
3x + y = 1
kx + 2y = 5
2y = 5 -kx
y = 5 -k/2
3x + y = 1
y = 1 - 3x.
These are the equivalent lines in the slope intercept form. Their slopes would be equal . If these lines were parallel and they would have no common point . Therefore , no solution for this type of equation .
slpoe intercept form y = mx + c
y = 5 - k/2
y = 1- 3x
-k/2 = -3
k = -3 * -2
k = 6.
so , the answer is 'there is no solution
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Step-by-step explanation:
3) the pair of linear equations are
Kx+2y=5=>Kx+2y-5=0
a1=k ; b1=2;c1=-5
and,3x+y=1=>3x+y-1=0
a2=3;b2=1;c2=-1
If the given lines have an unique solution then the condition is
a1/a2≠b1/b2
=>k/3≠2/1
=>k/3≠2
=>k≠6
the condition is k≠0
4) Given x=a and y=b is a solution of x-y=2 then
=>a-b=2=>a-b=-2...(1)
and x=a and y=b is a solution of x+y=4 then
=>a+b=4.....(2)
from (1)&(2)
a-b=-2
a+b=4
------------
2a=2
..............
=>2a=2
=>a=2/2=1
and 1+b=4=>b=4-1=3
Values of a=1 and b=3
If a point is a solution of the given equation then the point satisfies the given equation.