# 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.**

**a.**x + y = 3 ;3x – 2y = 4

**b.**2x + 4y = 10 ; 3x + 6y = 12

**c.**3x – y = 2 ; 9x – 3y = 6

**d.**ax + by = a - b ;bx -ay = a + b

**e.**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

**Q.6**If 5x + 7y = 3 and 15x + 21y = k represent coincident lines, then find the value of k.

**Q.7**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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