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11th Grade Math
Worksheet on Variables
This section contains worksheet on variables(two variables). Here you have to use substitution,elimination and cross multiplication method.
Q.1 Solve the following by elimination method.
a) 4x – 3y – 8 =0 ; 6x – y – 29/3 = 0
b) 2x + 3y = 8 ;4x + 6y = 7.
c) 2x + y -11 =0 ; x - y – 1=0
d) 8x + 5y = 9 ;3x + 2y = 4
e) 7(y + 3) - 2(x + 2 ) = 14 ; 4(y - 2)+3(x - 3) = 2
Q.2 Solve the following by cross- multiplication method.
x + y = 3 ;3x – 2y = 4
2x + 4y = 10 ; 3x + 6y = 12
3x – y = 2 ; 9x – 3y = 6
ax + by = a - b ;bx -ay = a + b
x + ay = b ax - by = c
Q.4 Find ‘k’.
1) If the equations have infinitely many solutions
2x + 3y = 4 ; ( k + 2) x + 6y = 3k + 2
kx -2y + 6 = 0 ;4x - 3y + 9 = 0
2)If the equations have no solutions
3x + y = 1 ; (2k –1)x + (k –1)y = 2k + 1
kx - 5y =2 ; 6x + 2y = 7
Q.5 Solve each system by substitution.
1) x -2y = 5 ;2x +3y = 10
2) 2x + y = 3 ; 2x – 3y = 7
3) x + y = 3 ; 2x +5y = 12
If 5x + 7y = 3 and 15x + 21y = k represent coincident lines, then find the value of k.
In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution,find it.
1) 2x + 3y = 7 ; 6x + 5y = 11
2) 6x + 5y =11 ; 9x + 15y/2 = 21
3) -3x + 4y = 5 ; 9x/2 - 6y + 15/2 = 0
Worksheet on variables
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