In the following figure, the measurements of side of rectangular ABCD is given. Find the values of $x$ and $y$.
- ✓$x=23, y=17$
- B$x=12, y=28$
- C$x=14, y=30$
- D$x=10, y=25$
Answer: A.
View full solution →Question types
Pair of Linear Equations in Two Variables question types
233 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
233
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
78 Q→02Fill In The Blanks[1 Marks ]
46 Q→03True False[1 Marks ]
27 Q→041 Marks Question
36 Q→052 Marks Questions
11 Q→063 Marks Question
17 Q→07Match The Following.
3 Q→084 Marks Questions
15 Q→Sample Questions
Pair of Linear Equations in Two Variables questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the following graph two lines are given
- ATheir solution is infinite.
- BThe solution of pair of equations is unique.
- CBy changing one variable in 10 another variable in solving pair of linear conditions is called method of substitution.
- ✓They have no solution
Answer: D.
View full solution →The sum of the ages of son and father before $5$ years was $30$ years. After $3$ years the sum of their ages will be ............
- ✓$46$
- B$40$
- C$50$
- D$38$
Answer: A.
View full solution →Which of the following method is used for the solution of pair of linear equations in two variables ?
- AGraphic Method
- BSubstitution Method
- CElimination
- ✓All of them
Answer: D.
View full solution →The ones of two digit is $x$ and tens is $y$, then the double of that digit is ..............
- A$10 x+2 y$
- B$2 y+20 x$
- ✓$20 y+2 x$
- D$2 x+10 y$
Answer: C.
View full solution →By Changing one variable in to another variable in solving pair of linear equations is called method of substitution. (Cramer rule, Elimination, Substitution)
The linear equations in two variables has infinite solutions if lines are ............. . (coincident, parallel, intersecting)
The sum of $5$ chairs and $2$ tables is $₹ 4850$, then from it the linear equations in two variables will be .............. .
$(5 x-2 y=48502 x+5 y=4850,5 x+2 y=4850)$
View full solution →$(5 x-2 y=48502 x+5 y=4850,5 x+2 y=4850)$
Normally, the condition that $a$ and $b$ both equally zero can be described by ............ .
$
\left(a^2-b^2 \neq 0, a^2+b^2 \neq 0,-a^2+b^2 \neq 0\right)
$
View full solution →$
\left(a^2-b^2 \neq 0, a^2+b^2 \neq 0,-a^2+b^2 \neq 0\right)
$
The sum of $1 kg$ tea and $7 kg$. sugar is $₹ 480$ , then from it the linear equation in two variables will be
$(x-7 y=480, x+7 y=480,7 x+y=480)$
View full solution →$(x-7 y=480, x+7 y=480,7 x+y=480)$
Point $(8,-2)$ lies in the fourth quadrant.
View full solution →The graph of the pair of equations $2 x+y=3$ and $4 x+2 y=6$ is a parallel line.
View full solution →$\frac{x}{2}=\frac{6}{y}=3$ then $x+y=8$.
View full solution →If $\frac{x}{2}+\frac{6}{x}=y$ is a linear equation in two variables.
View full solution →The graph of the equation $3 x+2=0$ is a line parallel to $X$-axis.
View full solution →Solve the pair of linear equations by substitution method: $3x – y = 3; 9x – 3y = 9$
View full solution →Is the pair of linear equation consistent/inconsistent? If consistent, obtain the solution graphically: $2x – 2y – 2 = 0; 4x – 4y – 5 = 0$
View full solution →Is the pair of linear equation consistent/inconsistent? If consistent, obtain the solution graphically: $x – y = 8; 3x – 3y = 16$
View full solution →On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equation is consistent, or inconsistent: $5x - 3y = 11; -10x + 6y = -22$
View full solution →On comparing the ratios $\frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } \text { and } \frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equations are consistent, or inconsistent: $\frac { 4 } { 3 } x + 2y = 8; 2x + 3y = 12.$
View full solution →A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $₹ 27$ for a book kept for seven days, while Susy paid $₹ 21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day. Solve the pair of the linear equation obtained by the elimination method.
View full solution →Five year 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? Solve by substitution method.
Solve the pair of linear equations by substitution method:
$\sqrt { 2 } x - \sqrt { 3 } y = 0$
$\sqrt { 3 } x - \sqrt { 8 } y = 0$
View full solution →$\sqrt { 2 } x - \sqrt { 3 } y = 0$
$\sqrt { 3 } x - \sqrt { 8 } y = 0$
On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac {c_1}{c_2}$, find out whether the pair of linear equations are consistent, or inconsistent: $ \frac { 3 } { 2 } x + \frac { 5 } { 3 } y = 7,$ $9x − 10y = 14$
View full solution →On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equations are consistent, or inconsistent: $2x − 3y = 8, 4x − 6y = 9.$
View full solution →Meena went to a bank to withdraw $₹ 2000$. She asked the cashier to give her $₹ 50$ and $₹ 100$ notes only. Meena got $25$ notes in all. Find how many notes of $₹ 50$ and $₹ 100$ she received. Solve the pair of the linear equation obtained by the elimination method.
View full solution →The sum of the digits of a two-digit number is $9$. Also, nine times this number is twice the number obtained by reversing the order of the number. Find the number. Solve the pair of the linear equation obtained by the elimination method.
View full solution →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? Solve the pair of the linear equation obtained by the elimination method.
If we add $1$ to the numerator and subtract $1$ from the denominator, a fraction reduces to $1$. It becomes $\frac 12$ if we only add $1$ to the denominator. What is the fraction? Solve the pair of the linear equation obtained by the elimination method.
View full solution →The larger of two supplementary angles exceeds the smaller by $18$ degrees. Find them by substitution method.
View full solution →| $A$ | $B$ |
| $Q.1.$ Mamta has $x$ five rupees notes and $y$ has ten rupees notes. If she has total $₹\ 155,$ then which equation is true for this data $?$ | $(a) x + 2y = 31$ |
| $Q.2.$ If the system of two variables linear equations are consistent then the lines are $.......$ | $(b) 2x + y = 31$ |
| $(c)$ Intersecting or coinciding. |
| $A$ | $B$ |
| $Q.1. ......$ is a two variable linear equation. | $(a) \frac{x}{2}+\frac{6}{x}=y$ |
| $Q.2.$ If the age of son is $\frac{1}{6}$ the age of his father then which equation is true for this data$?$ | $(b) x=y$ |
| $(c) x – 6y = 0$ |
| $A$ | $B$ |
| $Q.1.$ If $x + 2y = 5$ and $2x + y = 7$ then $x – y = .....$ | $(a) 2$ |
| $Q.2.$ The standard form of the equation $x-\frac{y}{2}=3$ is $......$ | $(b) 2x – y – 3 = 0$ |
| $(c) 2x – y – 6 = 0$ |
Solve the pairs of linear equation by the elimination method and the substitution method:$\frac{x}{2} + \frac{{2y}}{3} = - 1\,and\,x - \frac{y}{3} = 3$
View full solution →Solve the given pair of linear equation by the elimination method and the substitution method: $3x – 5y – 4 = 0$ and $9x = 2y + 7$
View full solution →Solve the given pair of linear equation by the elimination method and the substitution method: $3x + 4y = 10$ and $2x – 2y = 2$
View full solution →Solve the given pair of linear equation by the elimination method and the substitution method: $x + y = 5$ and $2x - 3y = 4$
View full solution →A fraction becomes $\frac { 9 } { 11 }$ if $2$ is added to both numerator and denominator. If $3$ is added to both numerator and denominator it becomes $ \frac { 5 } { 6 }$. Find the fraction by substitution method.
View full solution →Generate a Pair of Linear Equations in Two Variables paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.