Write whether the following pair of linear equations is consistent or not.
x + y = 14
x - y = 4
x + y = 14
x - y = 4
the equation have unique solution.
Pair of linear equations are consistent.
Find the value of k so that the following system of equations has infinite solutions:
3x - y - 5 = 0; 6x - 2y + k = 0
Here, a1 = 3, b1 = -1 and c1 = -5
a2 = 6, b2 = -2 and c2 = k
Hence the given system will have infinite no. of solution if k = -10.
The given pair of equation is
2x + 3y = 5
5x - 2y = 3
Putting x = 1,y = 1 in eq. (i) and (ii), we get
2x + 3y = 5
⇒ 2(1) + 3(1) = 5
⇒ 5 = 5 which is true.
Also, 5a - 2y = 3
⇒ 5(1) - 2(1) = 3
⇒ 3 = 3 which is true.
Thus, x = 1, y - 1 is the solution of the given pair of equations.
2x - 3y = 4; 4x - 6y = 7; 6x - 9y - 12.
Sol. Pair of infinite solutions :
2x - 3y = 4; 6x - 9y = 12
Here, a1 = 2, b1 = -3 and c1 = 4
and a2 = 6, b2 = -9 and c2 = 12
The given values satisfy the condition :
So, given equations have infinite solutions pair of no solutions :
2x - 3y = 4; 4x - 6y = 7
Here, a1 = 2, b1 = -3 and c1 = 4
and a2 = 4, b2 = -6 and c2 = 7
The given values satisfy the condition:
So, given equations have no solutions.
We have,
kx - 4y = 3; 6x - 12y = 9
Here, a1 = k, b = -4,c1 = 3
a2 = 6, b2 = - 12, c2 = 9
For infinitely many solutions,
Hence, the given system of equation has infinitely many solution if, k = 2.