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Linear Equations in Two Variables Maths - Linear Equations in Two Variables

Gujarat Board (GSEB) - STD 10 - Maths (GSEB - English Medium). 322 questions in this chapter.

Question types

Linear Equations in Two Variables question types

322 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

322
Questions
4
Question groups
5
Question types
Sample Questions

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.

Q 1M.C.Q (1 Marks)1 Mark
If the system of equations has infinitely many solutions, then:
$2x + 3y = 7$
$(a + b)x + (2a - b)y = 21$
  • A
    $a = 1, b = 5$
     
  • ✓
    $a = 5, b = 1$
     
  • C
    $a = -1, b = 5$
     
  • D
    $a = 5, b = -1$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
The value of $k$ for which the system of equations $x + 2y - 3 = 0$ and $5x + ky + 7 = 0$ has no solution, is:
  • ✓
    $10$
  • B
    $6$
  • C
    $3$
  • D
    $1$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
The sum of the digits of a two digit number is $9$. if $27$ is added to it, the digits of the number get reversed. The number is:
  • A
    $25$
  • B
    $72$
  • C
    $63$
  • ✓
    $36$

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark
If $am ≠ bl$, then the system of equations $ax + by = clx + my = nax + by = clx + my = n$.
  • ✓
    Has a unique solution.
     
  • B
    Has no solution.
     
  • C
    Has infinitely many solutions.
     
  • D
    May or may not have a solution.

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
If $2x - 3y = 7$ and $(a + b)x - (a + b - 3)y = 4a + b$ represent coincident lines, then $a$ and $b$ satisfy the equation:
  • A
    $a + 5b = 0$
  • B
    $5a + b = 0$
  • ✓
    $a - 5b = 0$
  • D
    $5a - b = 0$

Answer: C.

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Q 62 Marks Questions2 Marks
Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
Infinitely many solutions?
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Q 72 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
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Q 82 Marks Questions2 Marks
Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
a unique solutions?
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Q 92 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$
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Q 102 Marks Questions2 Marks
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$
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Q 133 Marks Question3 Marks
Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.
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Q 143 Marks Question3 Marks
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 $Rs. 50$ and $Rs. 100$ she received.
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Q 153 Marks Question3 Marks
The cost of $4$ pens and $4$ pencil boxes is $₹\ 100.$ Three times the cost of a pen is $₹\ 15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and pencil box.
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Q 164 Marks Questions4 Marks
$ABCD$ is a cyclic quadrilateral such that $\angle\text{A}=(4\text{y}+20)^\circ,\angle\text{B}=(3\text{y}-5)^\circ$ $\angle\text{C}=(-4\text{x})^\circ$ and $\angle\text{D}=(7\text{x}+5)^\circ$ Find the four angles.
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Q 174 Marks Questions4 Marks
Solve the following systems of equations:
$\frac{2}{3\text{x}+2\text{y}}+\frac{3}{3\text{x}-2\text{y}}=\frac{17}{5},$
$\frac{5}{3\text{x}+2\text{y}}+\frac{1}{3\text{x}-2\text{y}}=2.$
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Q 184 Marks Questions4 Marks
Solve graphically the following system of linear equation. Also find the coordinates of the points where the lines meet axis of y.
$3x + 2y = 12$
$5x - 2y = 4$
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Q 194 Marks Questions4 Marks
Represent the following pair of equations graphically and write the coordinates of points where the lines intersects $y-$axis.
$x + 3y = 6,$
$2x - 3y = 12.$
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Q 204 Marks Questions4 Marks
Akhila went to a fair in her village. She wanted to enjoy rides in the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs $Rs. 3,$ and a game of Hoopla costs $Rs. 4.$ If she spent $Rs. 20$ in the fair, represent this situation algebraically and graphically.
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