CBSE Questions for Class 10 Maths Pair Of Linear Equations In Two Variables Quiz 6 - MCQExams.com

Solve the following simultaneous equation. 
$$12x+17y=53; \, \, 17x+12y=63$$
  • $$x = 3,\, y=1$$
  • $$x = 2,\, y=1$$
  • $$x = 1,\, y=1$$
  • $$x = 9,\, y=1$$
Solve the following equations by substitution method.
$$2x+y=-2;\, \, 3x-y=7$$
  • $$x = 1, y= -4$$
  • $$x = 1, y= -1$$
  • $$x = 1, y= -3$$
  • $$x = 1, y= -5$$
If $$\displaystyle \frac{x+y-8}{2} = \frac{x+2y-14}{3}=\frac{3x-y}{4}$$, then the values of $$x$$ and $$y$$ is
  • $$x=1, \, y=3$$
  • $$x=5, \, y=2$$
  • $$x=3, \, y=3$$
  • $$x=2, \, y=6$$
Solve the following simultaneous equations by the method of equating coefficients.$$3x-4y=7;\, \, 5x+2y=3$$ .
  • $$x = 1, y= -1$$
  • $$x = 2, y= 1$$
  • $$x = 5, y= 2$$
  • $$x = 4, y= -3$$
From the following figure, we can say: 
$$\displaystyle \frac{x}{3}+\frac{y}{4}=4; \, \, \frac{5x}{6}-\frac{y}{8}=4 $$
  • $$x=1, \, y=8$$
  • $$x=7, \, y=8$$
  • $$x=6, \, y=8$$
  • $$x=3, \, y=8$$
Solve the following pair of equations. $$25x-24y=197; \, \,  24x-25y=195$$
  • $$x=1,\, y=-3$$
  • $$x=9,\, y=-3$$
  • $$x=5,\, y=-3$$
  • $$x=3,\, y=-3$$
The ratio of the present ages of mother and son is $$ 12: 5$$. The mother's age at the time of the birth of the son was $$21$$ years. Find their present ages.
  • mother age $$=$$ $$36$$ years, son age $$=$$ $$15$$ years
  • mother age $$=$$ $$56$$ years, son age $$=$$ $$5$$ years
  • mother age $$=$$ $$46$$ years, son age $$=$$ $$25$$ years
  • mother age $$=$$ $$47$$ years, son age $$=$$ $$26$$ years
Solve graphically:
$$\displaystyle 2x-3y=7 $$ and $$\displaystyle 5x+y=9$$
  • $$\displaystyle x=2,y=-6$$
  • $$\displaystyle x=8,y=-9$$
  • $$\displaystyle x=0,y=-3$$
  • $$\displaystyle x=2,y=-1$$
A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number.
  • 25
  • 45
  • 75
  • None of these
Point $$A$$ and $$B$$ are $$70\ km$$ apart on a highway. A car starts from $$A$$ and another car starts from $$B$$ at the same time. If they travel in the same direction, they meet in $$7$$ hours, but if they travel towards each other they meet in one hour. What are their speeds?
  • $$30\ km/hr$$ and $$40\ km/hr$$
  • $$36\ km/hr$$ and $$40\ km/hr$$
  • $$19\ km/hr$$ and $$20\ km/hr$$
  • $$40\ km/hr$$ and $$50\ km/hr$$
Solve the following simultaneous equation :
$$ax\, +\, by\, =\, 5$$ and $$\, bx\, +\, ay\, =\, 3,$$ where $$a$$ and $$b$$ are constants.
  •  $$\displaystyle x\, =\, \frac{5a\, -\, 3b}{a^2\, +\, b^2}, \quad\, y\, =\, \frac{3a\, -\, 5b}{a^2\, +\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{5a\, -\, 3b}{a^2\, -\, b^2}, \quad\, y\, =\, \frac{3a\, -\, 5b}{a^2\, -\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{3a\, -\, 5b}{a^2\, -\, b^2}, \quad\, y\, =\, \frac{5a\, -\, 5b}{a^2\, -\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{3a\, -\, 5b}{a^2\, +\, b^2}, \quad\, y\, =\, \frac{5a\, -\, 5b}{a^2\, +\, b^2}$$
The area of a rectangle gets reduced by $$9$$ sq. units, if its length is reduced by $$5$$ units and the breadth, is increased by $$3$$ units. If we increase the length by $$3$$ units and breadth by $$2$$ units, the area is increased by $$67$$ sq. units. Find the length and breadth of the rectangle. 
  • length $$ = 12$$, breadth $$=6$$
  • length $$ = 20$$, breadth $$=15$$
  • length $$ = 17$$, breadth $$=9$$
  • length $$ = 21$$, breadth $$=8$$
A man gets Rs. 100 per day if he works, but he is  fined by Rs. 10 per day if he is absent. In the whole month of April he received Rs. 1900 only. How many days did he work ? 
  • 20 days
  • 22 days
  • 29 days
  • 23 days
Solvw the following pair of linear equations:
 $$2x\, +\, 5y\, =\, 13$$ and $$4x\, -\, 9y\, =7$$
  • $$(1,4)$$
  • $$(2,-3)$$
  • $$(-2,3)$$
  • $$(4,1)$$
If $$12x\, +\, 13y\, =\, 29\, and\, 13x\, +\, 12y\, =\, 21,$$ find $$x\, +\, y$$.
  • $$2$$
  • $$7$$
  • $$4$$
  • $$11$$
In the following figure, $$ABCD$$ is a parallelogram. Find the values of $$x$$.

182362_4225d828fbb943ef83aa27b79c417d06.png
  • $$3$$
  • $$5$$
  • $$7$$
  • $$9$$
If $$1$$ is added to each of the two certain numbers, their ratio is $$1:2$$; and if $$5$$ is subtracted from each of the two numbers, their ratio becomes $$5:11$$. Find the numbers. 
  • $$35$$ and $$70$$
  • $$35$$ and $$71$$
  • $$35$$ and $$72$$
  • $$35$$ and $$73$$
Solve the following simultaneous equations:
$$8x+13y-29= 0$$, $$12x-7y-17= 0$$
  • $$x=3;\, y=2$$
  • $$x=0;\, y=5$$
  • $$x=2;\, y=1$$
  • $$x=-1;\, y=3$$
Solve the set of equations: $$3\left ( 2u+v \right )= 7uv$$ and $$3\left ( u+3v \right )= 11uv$$
  • $$u= 1; v= \displaystyle \frac{3}{2}$$
  • $$u= 2; v= \displaystyle \frac{1}{2}$$
  • $$u= 2; v= \displaystyle \frac{5}{4}$$
  • $$u= 5; v= \displaystyle \frac{7}{4}$$
A triangle is formed by the straight lines: $$\displaystyle x + 2y - 3 = 0, 3x - 2y + 7 = 0$$ and $$\displaystyle y + 1 = 0$$. 
Find graphically, the co-ordinates of the vertices of the triangle.
  • $$(-1,2), (5,-1), (-3,-1)$$
  • $$(-1,2), (7,4), (-3,-1)$$
  • $$(7,-4), (5,-1), (-3,-1)$$
  • $$(-12,5), (5,-1), (-3,-1)$$
Solve : $$\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$$ and $$\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$$
  • $$x\, =\, \displaystyle \frac{1}{7}\; \, y\, =\, \displaystyle \frac{1}{6}$$
  • $$x\, =\, \displaystyle \frac{3}{4}\; \, y\, =\, \displaystyle \frac{1}{6}$$
  • $$x\, =\, \displaystyle \frac{1}{4}\; \, y\, =\, \displaystyle \frac{1}{7}$$
  • $$x\, =\, \displaystyle \frac{2}{7}\; \, y\, =\, \displaystyle \frac{1}{7}$$
Solve the following simultaneous equations :
$$3x-5y+1= 0$$, $$2x-y+3= 0$$
  • $$x= 2;\, y= -1$$
  • $$x= 7;\, y= -9$$
  • $$x= -1;\, y= -4$$
  • $$x= -2;\, y= -1$$
Solve the following simultaneous equations:
$$3x+2y= 14$$, $$-x+4y= 7$$
  • $$x= 0;\, y= -4$$
  • $$x= 3;\, y= 2.5$$
  • $$x= 3.5;\, y= -2$$
  • $$x= 4.5;\, y= 3$$
Solve : $$\displaystyle \frac{3}{x+y}+\displaystyle \frac{2}{x-y}= 2$$ and $$\displaystyle \frac{9}{x+y}-\displaystyle \frac{4}{x-y}= 1$$
  • $$x= \displaystyle \frac{2}{5}; y= \displaystyle \frac{7}{2}$$
  • $$x= \displaystyle \frac{5}{2}; y= \displaystyle \frac{1}{2}$$
  • $$x= \displaystyle \frac{6}{7}; y= \displaystyle \frac{4}{3}$$
  • $$x= \displaystyle \frac{7}{3}; y= \displaystyle \frac{1}{2}$$
Solve: $$4x+\displaystyle \frac{6}{y}= 15$$ and $$6x-\displaystyle \frac{8}{y}= 14$$. Hence find the value of $$k$$, if $$y= kx-2$$.
  • $$x= 4, y= 1$$ and $$k= \displaystyle \frac{2}{3}$$
  • $$x= 5, y= 3$$ and $$k= \displaystyle \frac{3}{5}$$
  • $$x= 3, y= 2$$ and $$k= \displaystyle \frac{4}{3}$$
  • $$x= 1, y= 2$$ and $$k= \displaystyle \frac{9}{2}$$
Solve: $$3\left ( 2x+y \right )= 7xy$$ and $$3\left ( x+3y \right )= 11xy$$;  
where, $$x\neq 0, y\neq 0$$
  • $$x= 3; y= \displaystyle \frac{1}{2}$$
  • $$x= 1; y= \displaystyle \dfrac{3}{2}$$
  • $$x= 4; y= 2$$
  • $$x= 3; y= 4$$
Solve the following simultaneous equations:
$$12x+15y+18= 0$$, $$18x-7y+86= 0$$
  • $$x=-4;\, y=2$$
  • $$x=1;\, y=0$$
  • $$x=-3;\, y=5$$
  • $$x=4;\, y=1$$
Solve graphically, the following pairs of equations:
$$\displaystyle \frac{x + 1}{4} = \frac{2}{3}(1 - 2y)$$

$$\displaystyle \frac{2 + 5y}{3} = \frac{x}{7} - 2$$
  • $$x = 3, y = -1$$
  • $$x = 7, y = -1$$
  • $$x = 5, y = -1$$
  • $$x = 4, y = -1$$
Solve the following pair of equations:
$$3x\, -\, y\, =\, 23$$
$$\displaystyle \frac{x}{3}\, +\, \displaystyle \frac{y}{4}\, =\, 4$$
  • $$x\, =-\, 4\, ;\, y\, =\, 1$$
  • $$x\, =-\, 1\, ;\, y\, =\, 7$$
  • $$x\, =\, 9\, ;\, y\, =\, 4$$
  • $$x\, =\, 7\, ;\, y\, =\, 13$$
Solve the following pair of equations:
$$13 + 2y = 9x$$, $$3y = 7x$$
  • $$x=6$$; $$y =-7$$
  • $$x=5$$ ; $$ =13$$
  • $$x=-7$$; $$y =1$$
  • $$x=3$$; $$y =7$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 10 Maths Quiz Questions and Answers