CBSE Questions for Class 10 Maths Pair Of Linear Equations In Two Variables Quiz 4 - MCQExams.com

Solve the following simultaneous equations :
$$\displaystyle \frac{16}{x + y}\, +\, \frac{2}{x - y}\, =\, 1;\quad \frac{8}{x + y}\, -\, \frac{12}{x - y}\, =\, 7$$
  • $$x = 2 , y = 3$$
  • $$x = 6 , y = 1$$
  • $$x = 7 , y = 4$$
  • $$x = 3 , y = 5$$
Solve the following simultaneous equations by substitution method.
$$2x +3y= -4; \, \, x-5y =11$$
  • $$x=-1, \, y=2$$
  • $$x=1, \, y=-2$$
  • $$x=-1, \, y=-2$$
  • $$x=1, \, y=2$$
Find the values of $$x$$ and $$y$$, if 
$$\displaystyle \frac{2}{x}\, +\, \frac{6}{y}\, =\, 13;\quad \frac{3}{x}\, +\, \frac{4}{y}\, =\, 12$$
  • $$x\, =\,\displaystyle \frac{1}{6}\, ,\, y\, =\, \frac{2}{3}$$
  • $$x\, =\,\displaystyle \frac{1}{3}\, ,\, y\, =\, \frac{2}{3}$$
  • $$x\, =\,\displaystyle \frac{1}{7}\, ,\, y\, =\, \frac{2}{3}$$
  • $$x\, =\,\displaystyle \frac{1}{2}\, ,\, y\, =\, \frac{2}{3}$$
Find the values of the $$x+y$$ and $$x-y$$ from the examples given below without solving for x and y

$$4x+3y=24;\, \, 3x+4y=25$$
  • $$7$$ , $$-1$$
  • $$1$$ , $$-7$$
  • $$1$$ , $$7$$
  • $$-7$$ , $$-1$$
Sum of two numbers isIf the larger number is divided by the smaller, the quotient is 7 and the remainder isFind the numbers. 
  • $$75, 14$$
  • $$90, 14$$
  • $$75, 18$$
  • $$85, 12$$
Solve the following simultaneous equations :
$$\displaystyle \frac{1}{3x}\, +\, \frac{1}{5y}\, =\, \frac{1}{15};\quad \frac{1}{2x}\, +\, \frac{1}{3y}\, =\, \frac{1}{12}$$
  • $$x = 5, y = 3$$
  • $$x = 6, y = 6$$
  • $$x = 2, y = -2$$
  • $$x = 1, y = -5$$
A man starts his job with a certain monthly salary and a fixed increment every year. If his salary will be Rs. $$11000$$  after $$2$$  years and Rs. $$14000$$ after $$4$$ years of his service. What is his starting salary and what is the annual increment?
  • Starting salary is Rs. $$7500$$ and increment is Rs. $$2500$$
  • Starting salary is Rs.$$5000$$ and increment is Rs. $$1800$$
  • Starting salary is Rs. $$8000$$ and increment is Rs. $$1500$$
  • Starting salary is Rs. $$7000$$ and increment is Rs. $$1300$$
Solve following pair of equations by equating the coefficient method:
$$2x\, -\, y\, =\, 9$$
$$3x\, -\, 7y\, =\, 19$$
  • $$x=2$$ , $$y=1$$
  • $$x=4$$ , $$y=-1$$
  • $$x=3$$ , $$y=2$$
  • $$x=7$$ , $$y=-8$$
Solve the given pair of equations by substitution method:
$$x\, +\, 5y\, =\, 18$$
$$3x\, +\, 2y\, =\, 41$$
  • $$(13 , 1)$$
  • $$(1 , 3)$$
  • $$(12 , 17)$$
  • $$(9 , 16)$$
Solve the following pair of simultaneous equations:
$$4x\, -\, 3y\, =\, 8$$
$$3x\, -\, 4y\, =\, - 1$$
  • $$x=3,y=-1$$
  • $$x=5,y=4$$
  • $$x=-4,y=2$$
  • $$x=7,y=-6$$
Draw the graph of $$ 2x - y -1=0 $$ and $$ 2x + y= 9 $$ on the same graph. Use $$2\ \mathrm{ cm} = 1$$ unit on both axes.
Write down the co-ordinates of the point of intersection of the two lines.
  • $$ x=3.5,\:y=4 $$
  • $$ x=4.5,\:y=4 $$
  • $$ x=1.5,\:y=4 $$
  • $$ x=2.5,\:y=4 $$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{x}{3}\, =\, \frac{y}{2}\,;\, \frac{2x}{3}\, -\, \frac{y}{2}\, =\, 2$$
  • $$(-3 , 4)$$
  • $$(1 , 9)$$
  • $$(6 , 4)$$
  • $$(3 , 8)$$
Solve the given pair of equations by substitution method:
$$x\, +\, y\, =\, 11$$
$$x\, -\, y\, =\, -3$$
  • $$(4 , 6)$$
  • $$(3 , 11)$$
  • $$(4 , 7)$$
  • $$(6 , 2)$$
Solve the given pair of equations by substitution method:
$$4a\, -\, b\, =\, 10$$
$$2a\, +\, 3b\, =\, 12$$
  • $$a = 0, b = 5$$
  • $$a = 7, b = 6$$
  • $$a = 1, b = 7$$
  • $$a = 3, b = 2$$
Solve the given pair of equations by substitution method:
$$x\, -\, 4y\, =\, -8$$
$$x\, -\, 2y\, =\, 0$$
  • $$(2 , -1)$$
  • $$(7, -6)$$
  • $$(8 , 4)$$
  • $$(-3 , 6)$$
Solve the given pair of equations by substitution method:
$$2a\, +\, 3b\, =\, 6$$
$$3a\, +\, 5b\, =\, 15$$
  • $$a = 3, b = 2$$
  • $$a = -15, b = 12$$
  • $$a = 8, b = 15$$
  • $$a = -7, b = 3$$
Solve the given pair of equations by substitution method:
$$x\, +\, y\, =\, 0$$
$$y\, -\, x\, =\, 6$$
  • $$(2 , 7)$$
  • $$(-3 , 3)$$
  • $$(4 , 9)$$
  • $$(-6 , 2)$$
Solve the following pair of simultaneous equations:
$$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$$
  • $$x = - 7$$ and $$y = 3$$
  • $$x = 0$$ and $$y = 3$$
  • $$x = - 5$$ and $$y = 9$$
  • $$x = - 1$$ and $$y = 5$$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{8}{x}\, -\, \frac{9}{y}\, =\, 1;\,\frac{10}{x}\, +\, \frac{6}{y}\, =\, 7$$
  • $$x= 2;y= 3$$
  • $$x= 7;y= 5$$
  • $$x= 4;y= 6$$
  • $$x= 1;y= 7$$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$$
  • $$x= \displaystyle \frac{3}{2};y= \displaystyle \frac{3}{4}$$
  • $$x= \displaystyle \frac{1}{2};y= \displaystyle \frac{2}{3}$$
  • $$x= \displaystyle \frac{1}{3};y= \displaystyle \frac{1}{2}$$
  • $$x= \displaystyle \frac{2}{3};y= \displaystyle \frac{1}{2}$$
Solve the following pair of simultaneous equations:
$$\displaystyle\,3x\, +\, \frac{1}{y}\, =\, 13\, ;\, \frac{2}{y}\, -\, x\, =\, 5$$
  • $$\displaystyle \frac{2}{5}$$ and $$4$$
  • $$3$$ and $$\displaystyle \frac{1}{4}$$
  • $$7$$ and $$\displaystyle \frac{1}{7}$$
  • $$3$$ and $$\displaystyle \frac{3}{4}$$
A man's age is three times that of his son and in twelve years he will be twice as old as his son would be. What are their present ages?
  • Present age of man is $$60$$ years and

    Present age of son is $$20$$ years
  • Present age of man is $$45$$ years and

    Present age of son is $$15$$ years
  • Present age of man is $$54$$ years and

    Present age of son is $$18$$ years
  • Present age of man is $$36$$ years and

    Present age of son is $$12$$ years
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{6}{x}\, -\, \frac{2}{y}\, =\, 1\,;\, \frac{9}{x}\, -\, \frac{6}{y}\,=\, 0$$
  • $$x = 7, y = -4$$
  • $$x = 6, y = -4$$
  • $$x = =1, y = 2$$
  • $$x = 3, y = 2$$
Find two numbers whose sum is $$15$$ and difference is $$3$$.
  • $$13$$ and $$2$$
  • $$7$$ and $$8$$
  • $$9$$ and $$6$$
  • $$3$$ and $$12$$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{a}{4}\, -\, \frac{b}{3}\, =\, 0\,;\, \frac{3a\, +\, 8}{5}\, =\, \frac{2b\, -\, 1}{2}$$
  • $$a = -4.5, b = 12$$
  • $$a = 4, b = -5$$
  • $$a = 14, b = 10.5$$
  • $$a = 12, b = 11.5$$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{3}{a}\, +\, \frac{4}{b}\, =\, 2\,;\, \frac{9}{a}\, -\, \frac{4}{b}\, =\, 2$$
  • $$a= 3, b = 4$$
  • $$a = 1, b = -2$$
  • $$a = 5, b = -3$$
  • $$a = 0, b = 6$$
Find two numbers, which differ by $$7$$, such that twice the greater added to five times the smaller gives $$42$$.
  • $$19$$ and $$12$$
  • $$12$$ and $$5$$
  • $$11$$ and $$4$$
  • $$16$$ and $$9$$
Solve the following pair of simultaneous equations:
$$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$$
  • $$x=-6,y=7$$
  • $$x=-3,y=1$$
  • $$x=1,y=-1$$
  • $$x=2,y=0$$
Solve the following pairs of equations, graphically:
$$x = 0$$ and $$x + 3y = 6$$
  • $$(0,2)$$
  • $$(2,0)$$
  • $$(0,-2)$$
  • $$(-2,0)$$
Solve the following pairs of equations, graphically:
$$3x - 4y = 1$$ and $$x - 2y + 1 = 0$$
  • $$(-3, -2)$$
  • $$(-3, 2)$$
  • $$(3, -2)$$
  • $$(3, 2)$$
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