CBSE Questions for Class 10 Maths Pair Of Linear Equations In Two Variables Quiz 5 - MCQExams.com

Solve the following pairs of equations, graphically:
$$3x - 2y = 0$$ and $$y + 3 = 0$$
  • $$(-2, -3)$$
  • $$(2, -3)$$
  • $$(-2, 3)$$
  • $$(-3, -3)$$
Solve the following pairs of equations, graphically:
$$x + y = 0$$ and $$y = 5$$
  • $$(5, -5)$$
  • $$(-5, -5)$$
  • $$(-5, 5)$$
  • $$(5, 5)$$
Find a fraction which reduces to $$\displaystyle \frac{2}{3}$$ if the numerator and the denominator are each increased by $$1$$, and reduces to $$\displaystyle \frac{3}{5}$$ if the numerator and the denominator are each decreased by $$2$$.
  • $$\displaystyle \frac{13}{12}$$
  • $$\displaystyle \frac{11}{17}$$
  • $$\displaystyle \frac{9}{4}$$
  • $$\displaystyle \frac{13}{3}$$
$$A$$ is $$25$$ years older than $$B$$. In $$15$$ years, $$A$$ will be twice of $$B$$. Find the present ages of $$A$$ and $$B$$.
  • Present age of $$A$$ is $$40$$ years and

    Present age of $$B$$ is $$15$$ years
  • Present age of $$A$$ is $$37$$ years and

    Present age of B is $$12$$ years
  • Present age of $$A$$ is $$35$$ years and

    Present age of $$B$$ is $$10$$ years
  • Present age of $$A$$ is $$45$$ years and

    Present age of $$B$$ is $$20$$ years
Find the values of $$(x+y)$$ and $$(x-y) $$without actually solving for $$x$$ and $$y$$. 
$$13x+15y=114 \quad and  \quad15x+13y=110$$
  • $$x+y= 9, x-y= -2$$
  • $$x+y= 8, x-y= -2$$
  • $$x+y= 3, x-y= -2$$
  • $$x+y= 1, x-y= -2$$
A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.
  • Present age of father is $$44$$ years and Present age of son is $$20$$ years
  • Present age of father is $$42$$ years and Present age of son is $$18$$ years
  • Present age of father is $$60$$ years and Present age of son is $$36$$ years
  • Present age of father is $$48$$ years and Present age of son is $$24$$ years
Solve the following pairs of equations, graphically:
$$\displaystyle\,\frac{x}{2}\,-\,\frac{y}{3}\,=\,3$$ and $$x \,+ \,y \,=\, 1$$
  • $$(-4, 3)$$
  • $$(4, -3)$$
  • $$(-4, -3)$$
  • $$(4, 3)$$
Find the fraction such that it becomes $$\displaystyle \frac{1}{2}$$ if 1 is added to the numerator, and $$\displaystyle \frac{1}{3}$$ if 1 is added to the denominator.
  • $$\dfrac{3}{8}$$
  • $$\dfrac{1}{6}$$
  • $$\dfrac{8}{7}$$
  • $$\dfrac{7}{3}$$
Solve the following pair of equations:
$$7x+6y= 71$$
$$5x-8y= -23$$
  • $$x= -5;y= 4$$
  • $$x= 3,y= -2$$
  • $$x= 5,y= 6$$
  • $$x= 1,y= 3$$
Solve the following pair of equations:

$$\displaystyle \frac{6}{x}+\displaystyle \frac{4}{y}= 20, \displaystyle \frac{9}{x}-\displaystyle \frac{7}{y}= 10.5$$
  • $$x= \displaystyle \frac{3}{7};y= \displaystyle \frac{2}{3}$$
  • $$x= \displaystyle \frac{2}{5};y= \displaystyle \frac{2}{3}$$
  • $$x= \displaystyle \frac{5}{7};y= \displaystyle \frac{1}{3}$$
  • $$x= \displaystyle \frac{2}{5};y= \displaystyle \frac{1}{7}$$
Solve the following pair of equations using substitution method:
$$\displaystyle \frac{5y}{2}-\displaystyle \frac{x}{3}= 8$$
$$\displaystyle \frac{y}{2}+\displaystyle \frac{5x}{3}= 12$$
  • $$x= 2;y= 7$$
  • $$x= 6;y= 4$$
  • $$x= 7;y= 1$$
  • $$x= 8;y= 3$$
Solve the following equations by substitution method.
$$3y-2x=9; \, \, 2x+5y=15$$
  • $$x = 0, y= 2$$
  • $$x = 5, y= 2$$
  • $$x = 1, y= 3$$
  • $$x = 0, y= 3$$
Solve the following pair of equations:
$$4x+\displaystyle \frac{6}{y}= 15$$ and $$6x-\displaystyle \frac{8}{y}=14$$
  • $$x= 5;y= 6$$
  • $$x= 3;y= 2$$
  • $$x= 7;y= 4$$
  • $$x= 0;y= 6$$
Solve the following pair of equations :
$$x-y= 0.9$$ and $$\displaystyle \frac{11}{2\left ( x+y \right )}= 1$$
  • $$x= 1.5;y= 4$$
  • $$x= 3;y= 2.5$$
  • $$x= 5.2;y= 0.3$$
  • $$x= 3.2;y= 2.3$$
Solve the following pair of linear (simultaneous) equations by the method of elimination :
$$x+y= 7$$
$$5x+12y= 7$$
  • $$x= 11$$ and $$y=-4$$
  • $$x= 1$$ and $$y=7$$
  • $$x= 13$$ and $$y=6$$
  • $$x= 1$$ and $$y=-3$$
Solve the following pairs of equations, graphically :
$$4x + 3y = 1$$  and $$2x - y = 3$$
  • $$(1, 0)$$
  • $$(1, -1)$$
  • $$(2, -1)$$
  • $$(2, -3)$$
Solve the following pair of equations:

$$\displaystyle \frac{9}{x}-\displaystyle \frac{4}{y}= 8$$, $$\displaystyle \frac{13}{x}+\displaystyle \frac{7}{y}=101$$
  • $$x= \displaystyle \frac{2}{3};y= \displaystyle \frac{4}{3}$$
  • $$x= \displaystyle \frac{1}{4};y= \displaystyle \frac{1}{7}$$
  • $$x= \displaystyle \frac{5}{4};y= \displaystyle \frac{2}{5}$$
  • $$x= \displaystyle \frac{3}{2};y= \displaystyle \frac{6}{5}$$
Solve the following pair of equations:

$$2x-3y-3= 0$$, $$\displaystyle \frac{2x}{3}+4y+\displaystyle \frac{1}{2}= 0$$
  • $$x= \displaystyle \frac{13}{20},y= -\displaystyle \frac{7}{10}$$
  • $$x= \displaystyle \frac{17}{20},y= -\displaystyle \frac{1}{20}$$
  • $$x= \displaystyle \frac{1}{10},y= -\displaystyle \frac{7}{10}$$
  • $$x= \displaystyle \frac{21}{20},y= -\displaystyle \frac{3}{10}$$
Solve the following pairs of linear equations, graphically :
$$\displaystyle\,2x \,-\, 3y\, =\, -6\,$$ and $$x\, -\,\dfrac{y}{2}\,=\,1$$ 
  • $$(3, \,2)$$
  • $$(3, \,3)$$
  • $$(4, \,4)$$
  • $$(3, \,4)$$
Solve the following equations by substitution method.
$$x=2y-1; \, \, y=2x-7$$
  • $$x = 8, y= 3$$
  • $$x = 2, y= 3$$
  • $$x = 5, y= 3$$
  • $$x = 1, y= 3$$
Solve: $$\displaystyle \frac{3}{x}-\displaystyle \frac{2}{y}= 0$$ and $$\displaystyle \frac{2}{x}+\displaystyle \frac{5}{y}= 19$$. Hence, find $$a$$ if $$y= ax+3$$.
  • $$x=\displaystyle \frac{2}{3};y= \displaystyle \frac{5}{3}$$ and $$a= 6\displaystyle \frac{6}{5}$$
  • $$x=\displaystyle \frac{3}{4};y= \displaystyle \frac{1}{3}$$ and $$a= -4\displaystyle \frac{7}{3}$$
  • $$x=\displaystyle \frac{7}{2};y= \displaystyle \frac{8}{3}$$ and $$a= -7\displaystyle \frac{2}{9}$$
  • $$x=\displaystyle \frac{1}{2};y= \displaystyle \frac{1}{3}$$ and $$a= -5\displaystyle \frac{1}{3}$$
Solve the following equations by substitution method.
$$2x-3y=14; \, \, 5x+2y=16$$
  • $$x = 7, y= 1$$
  • $$x = 4, y= -2$$
  • $$x = 6, y= -2$$
  • $$x = 3, y= -1$$
Solve the following equations by substitution method.
$$x-2y+2=0; \, \, x+2y=10$$
  • $$x = 4, y= 3$$
  • $$x = 1, y= 3$$
  • $$x = 9, y= 3$$
  • $$x = 5, y= 3$$
Solve: $$\displaystyle \frac{34}{3x+4y}+\displaystyle \frac{15}{3x-2y}= 5$$ and $$\displaystyle \frac{25}{3x-2y}-\displaystyle \frac{8.50}{3x+4y}= 4.5$$
  • $$x= 1;y= 4$$
  • $$x= 3;y= 2$$
  • $$x= 5;y= 8$$
  • $$x= 7;y= 6$$
Solve: $$\displaystyle \frac{20}{x+y}+\displaystyle \frac{3}{x-y}= 7$$ and $$\displaystyle \frac{8}{x-y}-\displaystyle \frac{15}{x+y}= 5$$
  • $$x= 4;y= -7$$
  • $$x= 4;y= -4$$
  • $$x= 3;y= 2$$
  • $$x= 1;y= 6$$
Solve the following equations by substitution method:
$$5x-2y=13; \, \, 4x+3y=15$$
  • $$x=1,y=-3$$
  • $$x=3,y=1$$
  • $$x=-1,y=3$$
  • $$x=-1,y=-3$$
The sides of an equilateral triangle are given by $$x+3y$$;  $$3x+2y-2$$ and $$4x+\displaystyle \frac{1}{2}y+1$$ respectively. Find the lengths of the sides of the triangle.
  • $$15$$ units each
  • $$17$$ units each
  • $$12$$ units each
  • $$11$$ units each
Solve: $$4x+\displaystyle \frac{6}{y}= 15$$ and $$6x-\displaystyle \frac{8}{y}= 14$$. Hence, find $$a$$ if $$y= ax-2$$
  • $$x= 2;y= 26$$ and $$a= 2\displaystyle \frac{5}{3}$$
  • $$x= 3;y= 2$$ and $$a= 1\displaystyle \frac{1}{3}$$
  • $$x= 1;y= 5$$ and $$a= 2\displaystyle \frac{7}{3}$$
  • $$x= 5;y= 1$$ and $$a= 5\displaystyle \frac{1}{8}$$
Solve the following equations by substitution method.
$$2x-3y-3=7; \, \, 4x-5y-5=10$$
  • $$x = \displaystyle \frac{-7}{2}, y= -5$$
  • $$x = \displaystyle \frac{-3}{2}, y= -5$$
  • $$x = \displaystyle \frac{-1}{2}, y= -5$$
  • $$x = \displaystyle \frac{-5}{2}, y= -5$$
Pooja and Ritu can do a piece of work in $$\displaystyle 17\frac{1}{7}$$ days. If one day work of Pooja is three fourth of one day work of Ritu then find in how many days each alone will do the same work.
  • Pooja in 40 days and Ritu in 30 days
  • Pooja in 60 days and Ritu in 40 days
  • Pooja in 30 days and Ritu in 10 days
  • Pooja in 45 days and Ritu in 20 days
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