CBSE Questions for Class 10 Maths Pair Of Linear Equations In Two Variables Quiz 2 - MCQExams.com

Given that $$3x-y=-11$$ and $$4x+y=4$$. Calculate the value of $$x$$.
  • $$-7$$
  • $$-1$$
  • $$8$$
  • $$15$$
Given that $$4x-3y=6$$ and $$x-3y=-3$$, the value of $$y$$ is
  • $$-3$$
  • $$-2$$
  • $$\dfrac { 4 }{ 3 } $$
  • $$2$$
The sum of two numbers is equal to $$20$$ and their difference is $$2.5$$. Find the ratio of the numbers
  • $$9 : 7$$
  • $$7 : 9$$
  • $$3 : 5$$
  • $$2 : 7$$
Given that $$2y=-6$$ and $$x-3y=13$$, the value of $$x=$$________
  • $$\dfrac { 13 }{ 9 } $$
  • $$4$$
  • $$19$$
  • $$22$$
Fill in the blank: _______ system of linear equation has no solution.
  • Inconsistent
  • Consistent
  • Dependent
  • Empty
The ratio of income of two persons is $$9 : 7$$ and the ratio of their expenditure is $$4 : 3$$.   If each of them manages to save Rs. $$2000$$ per month, find their monthly income. 
  • $$Rs. 18,000 , Rs. 14,000$$ 
  • $$Rs. 1,000 , Rs. 14,000$$ 
  • $$Rs. 18,000 , Rs. 1,000$$ 
  • None of these
If $$(a+b,1)=(5,a-b)$$, then the value of $$2a+3b=$$?
  • $$5$$
  • $$12$$
  • $$8$$
  • $$6$$
To eliminate x from equations $$x + y + 3x = 12 \rightarrow$$ ....... (1) & $$8x + 3y = 17  \rightarrow $$ ..... (2), equation (2) is to be multiplied by ..............( from the given options)
  • 8
  • $$- \dfrac{1}{2}$$
  • 3
  • None of the above
Determine graphically the vertices of the triangle, the equations of whose side are give below:
$$y=x,y =0$$ and $$3x+3y=10$$
  • $$(0,0) \, \left(\dfrac{10}{3},0\right)\, \left(\dfrac{5}{3}, \dfrac{5}{3}\right)$$
  • $$(0,0) \, \left(\dfrac{17}{3},0\right)\, \left(\dfrac{5}{3}, \dfrac{5}{3}\right)$$
  • $$(0,0) \, \left(\dfrac{14}{3},0\right)\, \left(\dfrac{5}{3}, \dfrac{5}{3}\right)$$
  • $$(0,0) \, \left(\dfrac{10}{3},0\right)\, \left(\dfrac{5}{3}, \dfrac{8}{3}\right)$$
The solution of $$8x+5y=9$$, $$3x+2y=4$$ lie on $$x+y=k$$, then $$k=$$
  • $$3$$
  • $$4$$
  • $$5$$
  • $$2$$
The solution of $$\sqrt{2}x+\sqrt{3}y=0$$ and $$\sqrt{3}x+\sqrt{8}y=0$$ is
  • $$(1, 2)$$
  • $$(\sqrt{2}, \sqrt{8})$$
  • $$(0, 0)$$
  • $$(\sqrt{3}, \sqrt{2})$$
If $$7$$ pens and $$3$$ books cost $$Rs 1395$$, while $$5$$ pens and $$4$$ books cost $$Rs 1665$$. Find the cost of a  book
  • $$360$$
  • $$45360$$
  • $$35350$$
  • $$none\ of\ these$$
The cost of $$4$$ pens and $$4$$ pencil boxes is Rs $$100$$. Three times the cost of a pen is Rs $$15$$ more than the cost of a pencil box. The cost of a pen and a pencil box respectively are 
  • Rs $$15$$ and Rs $$8$$
  • Rs $$10$$ and Rs $$15$$
  • Rs $$12$$ and Rs $$10$$
  • Rs $$16$$ and Rs $$12$$
The sum of two numbers is $$2$$ and their difference is $$1$$. Find the numbers.
  • $$2,0$$
  • $$1.5,0.5$$
  • $$1,1$$
  • $$-0.5,2.5$$
Solve:
$$4x + \frac{6}{y} = 15$$
$$6x - \frac{8}{y} = 14$$
  • $$x=-3,y=2$$
  • $$x=2,y=3$$
  • $$x=3,y=-2$$
  • $$x=3,y=2$$
To eliminate x, from $$3x+y=7$$ and $$-x+2y=2$$ second equation is multiplied by ______
  • $$1$$
  • $$3$$
  • $$2$$
  • $$-1$$
 Solve for $$x$$ and $$y$$ by using method of substitution :
$$0.2x+0.3y=1.3$$; $$0.4x+0.5y=2.3$$
  • $$-2,-3$$
  • $$2,-3$$
  • $$2,3$$
  • $$-2,3$$
Solve 
$$5x-4y+8=0$$
$$7x+6y-9=0$$.
  • $$x = \cfrac{6}{29}$$ and $$y = -\cfrac{101}{58}$$

  • $$x = -\cfrac{6}{29}$$ and $$y = \cfrac{101}{58}$$

  • $$x = -\cfrac{8}{29}$$ and $$y = \cfrac{101}{58}$$

  • None of these
Solve : $$ ax + by = a - b$$
             $$bx - ay = a + b$$
  • $$x=a,y=-b$$
  • $$x=1,y=-1$$
  • $$x=-1,y=1$$
  • $$x=\dfrac {1}{a},y=-\dfrac {1}{b}$$
Solve $$0.2x+0.3y=1.3$$ 
$$0.4x+0.5y=2.3$$
  • $$x=-2$$ and $$y=3$$
  • $$x=3$$ and $$y=3$$
  • $$x=2$$ and $$y=3$$
  • None of these
Given two straight lines $$x + y - 7 = 0$$ and $$x - y + 3 = 0$$ . Find point of intersection of them.
  • $$(2,5)$$
  • $$(-2,-5)$$
  • $$(2,-5)$$
  • $$(-2,5)$$
The graph of the linear equation $$2x + 3y = 6$$ is a line which meets the $$x-$$axis at the point
  • $$(0, 2)$$
  • $$(2, 0)$$
  • $$(3, 0)$$
  • $$(0, 3)$$
If  $$2x + y = 23$$  and  $$4x - y = 19$$, find the values of  $$5y -  2x$$ 
  • $$31$$
  • $$22$$
  • $$65$$
  • $$10$$
The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father respectively are
  • $$4$$ and $$24$$
  • $$5$$ and $$30$$
  • $$6$$ and $$36$$
  • $$3$$ and $$24$$
The graph of the linear equation $$2x + 3y = 6$$ intersects the $$y-$$axis at the point
  • $$(2, 0)$$
  • $$(0, 3)$$
  • $$(3, 0)$$
  • $$(0, 2)$$
Determine the vertices of the triangle formed by the lines
$$y = x, 3y = x $$ and $$  x + y = 8$$.
  • $$(0, 0), (0, 4), (6, 2)$$
  • $$(0, 0), (4, 4), (0, 2)$$
  • $$(0, 0), (7, 7), (5, 2)$$
  • $$(0, 0), (4, 4), (6, 2)$$
Are the following pair of linear equations consistent? 
$$-3x-4y=12$$, 
$$ 4y+3x=12$$
  • No
  • Yes
  • Data Insufficient
  • None of these
The values of x and y satisfying the two equations $$32x + 33y = 31$$, $$33x + 32y = 34$$ respectively will be
  • $$- 1, 2$$
  • $$2, - 1$$
  • $$0, 0$$
  • $$2, 3$$
If $$x=a, y=b$$ is the solution of the equations $$x-y=2$$ and $$x+y=4$$, then the values of $$a$$ and $$b$$ are, respectively:
  • $$3$$ and $$5$$
  • $$5$$ and $$3$$
  • $$3$$ and $$1$$
  • $$-1$$ and $$-3$$
The solution of
$$217x+131y=913$$
$$131x+217y=827$$  is
  • $$x=2, y=3$$
  • $$x=3, y=2$$
  • $$x=2, y=2$$
  • $$x=3, y=3$$
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