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

Draw the graphs of the equations $$x = 3, x = 5$$ and $$2x - y - 4 = 0$$. Also find the area of the quadrilateral formed by the lines and the x-axis
  • $$2$$ sq. unit
  • $$8$$ sq. unit
  • $$15$$ sq. unit
  • $$20$$ sq. unit
A and B each have a certain number of mangoes. A says to B," if you give 30 of your mangoes, I will have twice as many as left with you."B replies,"if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
  • A : $$34$$ mangoes; B : $$62$$ mangoes
  • A : $$22$$ mangoes; B : $$48$$ mangoes
  • A : $$38$$ mangoes; B : $$90$$ mangoes
  • A : $$56$$ mangoes; B : $$92$$ mangoes
Solve:

$$\dfrac {3x-2}{3y+7}=\dfrac {5x-1}{5y+16}; \dfrac {3x-15}{x-9}=\dfrac {6y-5}{2y+3}$$
  • $$x = 1, y = 4$$
  • $$x = 3, y = 2$$
  • $$x = 7, y = 4$$
  • $$x = 6, y = 5$$
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn't this interesting?) What are their present ages? Solve graphically introducing necessary varaibles.
  • $$12, 42$$
  • $$13, 47$$
  • $$18, 51$$
  • None of these
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. $$27$$ for a book kept for seven days, while Susy paid Rs. $$21$$ for the book she kept for five days. Find the fixed charge and the charge for each extra day.
  • Fixed charge: Rs. $$12$$, Charge for each extra day: Rs. $$9$$
  • Fixed charge: Rs. $$15$$, Charge for each extra day: Rs. $$3$$
  • Fixed charge: Rs. $$18$$, Charge for each extra day: Rs. $$3$$
  • Data insufficient
One says," give me a hundred, friend! I shall then become twice as rich as you," The other replies," If you give me ten, I shall be six times as rich as you." Tell me what is the amount of their respective capital?
  • $$70 \ and \ 160$$
  • $$66\  and \ 190$$
  • $$40 \ and \ 170$$
  • $$30 \ and \ 120$$
Solve the following pair of linear equations by the substitution method
$$x + y = 14, x - y = 4$$
  • $$x = 8, y = 5$$
  • $$x = 6, y = 9$$
  • $$x = 7, y = 10$$
  • None of these
On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the following pairs of linear equations are consistent, or inconsistent.
$$5x - 3y = 11; - 10x + 6y =  22$$
  • Consistent
  • Inconsistent
  • Ambiguous
  • Data insufficient
On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the following pairs of linear equations are consistent, or inconsistent.
$$2x - 3y = 8; 4x - 6y = 9$$
  • Consistent
  • Inconsistent
  • Ambiguous
  • Data insufficient
Determine whether the following pair of linear equations are consistent/inconsistent.
 $$2x - 2y - 2 = 0, 4x - 4y - 5 = 0$$
  •  The graph is coincident straight line.
  •  The graph is intersecting lines.
  • Inconsistent
  • Data insufficient
Draw the graphs of the equations $$x - y + 1 = 0$$ and $$3x + 2y - 12 = 0$$. Determine the co-ordinates of the vertices of the triangle formed by these lines and the $$x$$-axis, and shade the triangular region.
  • $$A (1,3), B (-1, 6)$$ and $$C (4, 0)$$
  • $$A (2,5), B (-1, 6)$$ and $$C (2, 0)$$
  • $$A (-2,5), B (-1, 6)$$ and $$C (2, 0)$$
  • $$A (2,3), B (-1, 0)$$ and $$C (4, 0)$$
Determine whether the following pairs of linear equations are consistent/inconsistent. 
$$x-y=8, 3x-3y= 16$$
If consistent, obtain the solution graphically.
  •  The graph is coincident straight line.
  •  The graph is intersecting lines.
  • Inconsistent
  • None of these
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
Meena went to a bank to withdraw Rs. $$2000.$$ She asked the cashier to give her Rs. $$50$$ and Rs. $$100$$ notes only. Meena got $$25$$ notes in all. Find how many notes of Rs. $$50$$  and Rs. $$100$$  she received
  • $$15$$  notes of Rs. $$50$$  and $$18$$  notes of Rs. $$100.$$
  • $$12$$  notes of Rs. $$50$$  and $$18$$ notes of Rs. $$100$$.
  • $$8$$ notes of Rs. $$50$$ and $$25$$  notes of Rs. $$100.$$
  • $$10$$ notes of Rs. $$50$$ and $$15$$ notes of Rs. $$100$$.
$$10$$ students of class $$X$$ took part in a Mathematics quiz. If the number of girls is $$4$$ more than the number of boys, find the number of boys and girls who took part in the quiz by graphical method.
  • $$2, 7$$
  • $$6, 9$$
  • $$3, 12$$
  • None of these
$$5$$ pencils and $$7$$ pens together cost Rs. $$50$$, whereas $$7$$ pencils and $$5$$ pens together cost Rs. $$46$$. Find the cost of one pencil and that of one pen by graphical method.
  • Cost of one pencil $$=$$ Rs. $$2$$ and that of one pen $$=$$ Rs. $$4$$
  • Cost of one pencil $$=$$ Rs. $$3$$ and that of one pen $$=$$ Rs. $$5$$
  • Cost of one pencil $$=$$ Rs. $$5$$ and that of one pen $$=$$ Rs. $$6$$
  • Cost of one pencil $$=$$ Rs. $$2$$ and that of one pen $$=$$ Rs. $$6$$
On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
$$6x - 3y + 10 = 0; 2x - y + 9 = 0$$
  • Intersect at a point
  • Parallel
  • Coincident
  • Data insufficient
On comparing the ratios $$\frac {a_1}{a_2}, \frac {b_1}{b_2}$$ and $$\frac {c_1}{c_2}$$, find out whether the lines representing the following pairs of linear equations intersect at a point, or are parallel or coincident.
$$9x + 3y + 12 = 0; 18x + 6y + 24 = 0$$
  • Intersect at a point
  • Parallel
  • Coincident
  • Cannot be determined
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs.What are the fixed charges and the charge per kilometer? How much does a person have to pay for traveling a distance of 25 km?
  • Fixed charge is Rs.$$5$$ and the charge per kilometer is Rs.$$10$$ For $$25$$ km person have to pay Rs.$$255$$.
  • Fixed charge is Rs.$$10$$. and the charge per kilometer is Rs.$$5$$. For $$25$$ km person have to pay Rs$$135$$.
  • Fixed charge is  Rs. $$15$$  and the charge per kilometer is  Rs. $$5$$. For $$25$$ km person have to pay Rs.$$140$$.
  • Fixed charge is 
    Rs.$$50$$. and the charge per kilometer is Rs$$20$$. For $$25$$ km person have to pay Rs$$50$$
Form the pair of linear equations for the following problem and find their solution by substitution method.
The difference between the two numbers is $$26$$ and one number is three times the other.
  • $$x - y = 26$$ and $$x = 3y$$,  $$x=33$$ and $$,y=11$$
  • $$x - y = 26$$ and $$x = 3y$$,  $$x=39$$ and $$y=13$$
  • $$x - y = 13$$ and $$x = 3y$$,  $$x=75$$ and $$y=25$$
  • None of these
Solve the following pair of linear equations by the substitution method.
$$\dfrac {3x}{2}-\dfrac {5y}{3}=-2,\,\, \dfrac {x}{3}+\dfrac {y}{2}=\dfrac {13}{6}$$
  • $$x=3,  y=3$$
  • $$x=1,  y=3$$
  • $$x=2,  y=3$$
  • $$x=0,  y=0$$
Solve the following pair of linear equations by the substitution method
$$s-t=3, \dfrac {s}{3}+\dfrac {t}{2}=6$$
  • $$s = 2, t = 7$$
  • $$s = 9, t = 6$$
  • $$s = 3, t = 1$$
  • $$s = 6, t = -9$$
A fraction becomes $$\dfrac {9}{11}$$, if $$2$$ is added to both the numerator and the denominator. If $$3$$ is added to both the numerator and the denominator it becomes $$\dfrac {5}{6}$$. Find the fraction.
  • $$\dfrac{7}{9}$$
  • $$\dfrac{5}{7}$$
  • $$\dfrac{9}{11}$$
  • None of these
Five years hence, the age of jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
  • Present age of Jacob: $$50$$ years and Present age of Jacob's son: $$15$$ years
  • Present age of Jacob: $$50$$. years and Present age of Jacob's son: $$10$$ years
  • Present age of Jacob: $$40$$ years and Present age of Jacob's son: $$10$$ years
  • Present age of Jacob: $$35$$  years and Present age of Jacob's son: $$15$$ years
Form the pair of linear equations for the following problem and find their solution by substitution method.
The larger of two supplementary angles exceeds the smaller by $$18$$ degrees. 
  • $$x + y = 100$$ and $$x - y = 18$$,  $$x=90$$ and $$\,y=16$$
  • $$x + y = 60$$ and $$x - y = 18$$,  $$x=95$$ and $$\,\,y=70$$
  • $$x + y = 180$$ and $$x - y = 18$$,  $$x=99$$ and $$\,\,y=81$$
  • None of these
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
  • Nuri is $$40$$ years old and Sonu is$$ 10 $$years old.
  • Nuri is $$50$$ years old and Sonu is$$ 20$$ years old.
  • Nuri is $$70$$  years old and Sonu is $$30$$ years old.
  • Nuri is $$60$$ years old and Sonu is $$10$$ years old.
Solve the following pair of equations by reducing them to a pair of linear equations:

$$\dfrac {1}{(x-1)}+\dfrac {1}{(y-2)}=2, \ \dfrac {6}{(x-1)}-\dfrac {2}{(y-2)}=1$$
  • $$x=\dfrac{11}{5},\,\,y=\dfrac{13}{11}$$
  • $$x=\dfrac{13}{5},\,\,y=\dfrac{30}{11}$$
  • $$x=\dfrac{4}{5},\,\,y=\dfrac{20}{11}$$
  • None of these
Solve the following pairs of equations by reducing them to a pair of linear equations:
$$\displaystyle \dfrac {7x-2y}{xy}=5, \dfrac {8x+7y}{xy}=15$$
  • $$x=0,\,\,y=2$$
  • $$x=2,\,\,y=7$$
  • $$x=13,\,\,y=0$$
  • $$x=1,\,\,y=1$$
The real numbers $$x$$ and $$y$$ are such that $$\displaystyle x+\frac{2}{y}=\frac{8}{3}$$ and $$\displaystyle y+\frac{2}{x}=3$$ . 
The value of $$xy$$, is 
  • $$\displaystyle \frac{4}{3}$$
  • $$\displaystyle \frac{16}{9}$$
  • $$2$$
  • $$4$$
Solve the following pair of equations by reducing them to a pair of linear equations:
$$\displaystyle \frac {2}{\sqrt x}+\frac {3}{\sqrt y}=2, \frac {4}{\sqrt x}-\frac {9}{\sqrt y}=-1$$
  • $$x=1,\,\,y=4$$
  • $$x=3,\,\,y=2$$
  • $$x=4,\,\,y=9$$
  • $$x=16,\,\,y=25$$
For which values of $$a$$ and $$b$$ does the following pair of linear equations have an infinite number of solutions?
$$2x + 3y = 7$$
$$(a - b)x + (a + b) y = 3 a + b - 2$$
  • $$a=1$$ and $$b=7$$
  • $$a=13$$ and $$b=6$$
  • $$a=2$$ and $$b=10$$
  • $$a=5$$ and $$b=1$$
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