Linear Equation in two variables

Q1. Which of the following option is true:

y=3x+5 has

Aa unique solution

B3 solutions

C2 solutions

Dinfinitely many solutions

Q2. 3x+10 will have:

AUnique solution

BTwo solutions

CInfinitely many solutions

DNo solution

Q3. The solution of the equation 2x+y=7 is:

A(0,5)

B(5,1)

C(1,5)

D(3,2)

Q4. The solution of the equation x=4y is:

A(4,1)

B(1,4)

C(-1,-4)

D(-1,4)

Q5. The solution of the equation πx+y=9 is:

A(9,0)

B(0,9)

C(-9,1)

D(1,-9)

Q6. If (2,1) is the solution of the equation 2x+3y=k, then the value of k is:

A7

B6

C-7

D9

Q7. Which of the following is a solution of the equation x-2y=4?

A(0,2)

B(1,1)

C(4,0)

D(2,0)

Q8. If (4,19) is a solution of the equation y=ax+3, then equals:

A3

B4

C5

D6

Q9. If (a,4) lies in 3x+y=10, then the value of 'a' is:

A3

B1

C2

D4

Q10. How many linear equations are satisfied by x=2 and y=-3?

AOnly one

BTwo

CThree

DInfinitely many

Q11. If x=-1,y=2 is a solution of the equation 2x-y=6, then the value of k is:

A1

B3

C5

D6

Q12. The solution of the equation 3x+4y=7 is:

A(1,1)

B(-1,1)

C(1,-1)

D(0,1)

Q13. The solution of the equation x=6y is:

A(6,1)

B(2,3)

C(3,-2)

D(1,6)

Q14. The solution of the equation x=6y is:

A(-2,\( \frac{3}{2} \))

B(2,\( \frac{1}{3} \))

C(0,2)

D(\( \frac{1}{3} \),2)

Q15. The solution of the equation 3x+4y=7 is:

A(-3,4)

B(3,4)

C(4,3)

D(4,2)

Q16. Which of the following is not a solution of 2x+y=7?

A(0,7)

B(1,5)

C(2,3)

D(3,2)

Q17. Which of the following is not a solution of x=4y?

A(0,0)

B(1,4)

C(4,1)

D(1,0)

Q18. x=3, y=-2 is a solution of the equation

Ax+y=5

B3x-2y=11

C4x-3y=18

D3x+y=5

Q19. If (2,0) is the solution of the linear equation 2x+3y=k, then the value of k is :

A4

B6

C5

D2

Q20. If (1,1) is a solution of the equation 5x+2ky=3k, then the value of k is:

A3

B4

C5

D6

Q21. The equation of x-axis is of the form:

Ax=0

By=0

Cx+y=0

Dx=y

Q22. The equation x=7 in two variables can be written as:

A0x+0y=7

B0x+1y=7

C1x+1y=7

D1x+0y=7

Q23. The graph if the linear equation 2x+3y=6 cuts the y-axis at the point:

A(3,0)

B(0,3)

C(0,2)

D(2,0)

Q24. The equation 5y=2 can be written as an equation in two variables as:

Ax+5y=2

B5y-2=0

Cx-5y-2=0

D0x+5y-2=0

Q25. Expressing y=2 in the form ax+by+c=0, the value of 'a' equals:

A0

B1

C2

D-2

Q26. Any point on the line y=x is of the form:

A(a,0)

B(a,a)

C(0,a)

D(a,-a)

Q27. Tiya went to a stationery shop to buy some pen. The cost of the ball pen was ₹5 less than half of the cost of a fountain pen. The given information expressed as a linear equation in two variables is:

Ax+5y+0=0

Bx-5y+0=0

C2x=5y

Dx-\( \frac{y}{2} \)-5=0

Q28. A student bought some books and pens. The cost of the book was ₹20 more than the cost of a pen. The linear equation taking the cost of book as ₹b and cost of pen as ₹p is:

Ab+2p-20=0

Bb-2p-20=0

Cb+p=0

Db-p=0

Q29. The equation y=k in two variables can be written as:

AOx+1y=k

B1x+1y=k

C1y+1k=0

D1y-1k=0

Q30. The standard form of the linear equation y-x in two variables is:

A1x+1y-7=0

B1x-1y-7=0

C-1x+1y-7=0

D1x+1y+7=0

Q31. In the equation 2x=-5y, the values of a,b,and c respectively are:

A2,-5,0

B-2,5,0

C2x,-5y,0

D2,5,0

Q32. Any equation in the form ax+by+c=0 where a,b and c are real numbers and a, b≠0, is called a :

ALinear equation in 3 variables

BLinear equation in 5 variables

CLinear equation in 2 variables

DLinear equation in real numbers

Q33. In a ODI cricket match between India and Sri Lanka played in Mumbai, two Indian batsmen together scored 176 runs.

Which equation satisfies the above equation?

Ax+176=y

Bx+y=176

Cy+176=x

Dxy=176

Q34. On his birthday, Nito donated 4 chocolates each to children and 3 chocolates to adults in a small orphanage centre. Teh linear equation representing the above situation if he distributed 50 total chocolates is:

Ax-y=50

B4x+3y=50

Cx-3y=50

D3x+4y=50

Q35. For the equation x=y, the values of a,b ans c are:

A1,1 and 1

B1,-1 and 0

C1,1 and 0

D-1,-1 and 0

Q36. If a=3, b=-5 and c=4, then which one is the correct linear equation in two variables?

A3x+4=-5y

B3x+4=5y

C3x-5y=4

D3x=-5y+4

Q37. Mary's mother went to the local market to buy some groceries. She found that the cost of 1 kg of potato was 10 times the cost of 1 kg of tomato. The linear equation satisfying the situation is:

Ax+y=10

Bx-y=10

Cxy=10

Dx-10y=0

Q38. The equation of y-axis is of the form:

Ax=0

By=0

Cx=y

Dx+y=0

Q39. The linear equation 2x=5y-7 can be written as:

A2x+5y-7=0

B2x+5y=7

C2x-5y-7=0

D2x-7=5y

Q40. The point (a,a) satisfies which equation?

Ax+y=k

Bx=y

Cx-y=k

DAll of the above