$a x+b y=c$ and $m x+n y=d$ and $a n \neq b m$ then these simultaneous equations have -
- ✓Only one common solution
- BNo solution
- CInfinite number of solutions
- DOnly two solutions
Answer: A.
View full solution →Question types
P-1 Linear Equations in Two Variables question types
283 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
283
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
55 Q→02Complete the following activities and rewrite it : (2M)
5 Q→032 Marks Questions
27 Q→04Complete the following activities and rewrite it ( 3 marks)
13 Q→05Complete the following activities and rewrite it :
6 Q→063 Marks Question
109 Q→074 Marks Questions
62 Q→081 Marks Question
6 Q→Sample Questions
P-1 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.
To solve x + y = 3; 3x–2y – 4 = 0 by determinant method find D.
- A5
- B1
- ✓-5
- D-1
Answer: C.
View full solution →Find the value of $\left|\begin{array}{cc}5 & 3 \\ -7 & -4\end{array}\right|$
- A$-1$
- B$-41$
- C$41$
- ✓$1$
Answer: D.
View full solution →For simultaneous equations in variables $x$ and $y, D_X=49, D_Y=-63, D=7$, then what is $x$ ?
- ✓$7$
- B$-7$
- C$1/7$
- D$-1/7$
Answer: A.
View full solution →To draw graph of $4x+5y=19$, Find y when $x = 1.$
- A$4$
- ✓$3$
- C$2$
- D$-3$
Answer: B.
View full solution →Complete the following table to draw the graph of $2x – 6y = 3$
View full solution →Fill in the blanks with correct number
$\left|\begin{array}{ll}
3 & 2 \\
4 & 5
\end{array}\right|=3 \times \square-\square \times 4=\square-8=\square$
View full solution →$\left|\begin{array}{ll}
3 & 2 \\
4 & 5
\end{array}\right|=3 \times \square-\square \times 4=\square-8=\square$
Fill in the blanks with correct number
$\left|\begin{array}{ll}3 & 2 \\ 4 & 5\end{array}\right|=3 \times \square-\square \times 4=\square-8=\square$
View full solution →$\left|\begin{array}{ll}3 & 2 \\ 4 & 5\end{array}\right|=3 \times \square-\square \times 4=\square-8=\square$
....(2)Solve the following simultaneous equation.
$49x – 57y = 172; 57x – 49y = 252$
View full solution →$49x – 57y = 172; 57x – 49y = 252$
Solve the following simultaneous equation.
99x + 101 y = 499; 101x + 99y = 501
99x + 101 y = 499; 101x + 99y = 501
Solve the following simultaneous equation.
$\frac{1}{3} x+y=\frac{10}{3} ; 2 x+\frac{1}{4} y=\frac{11}{4}$
View full solution →$\frac{1}{3} x+y=\frac{10}{3} ; 2 x+\frac{1}{4} y=\frac{11}{4}$
Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4
5x + 2y = –3; x + 5y = 4
Solve the following simultaneous equation.
5m – 3n = 19; m – 6n = –7
5m – 3n = 19; m – 6n = –7
Solve the following word problems.
A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
There are some instructions given below. Frame the equations from the information and write them in the blank boxes shown by arrows.
Complete the following table.
Solve the following word problems.
A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
Let the digit in unit’s place is x
and that in the ten’s place is y
the number = ⬜y + x
The number obtained by interchanging the digits is ⬜x + y
According to first condition two digit number + the number obtained by interchanging the digits = 143
∴ 10y + x = 143
∴ ⬜x + ⬜y = 143
x + y = ⬜......(I)
From the second condition,
digit in unit’s place = digit in the ten’s place + 3
∴ X = ⬜ + 3
∴ X - Y= 3.....(II)
Adding equations (I) and (II)
2X = ⬜
X = 8
Putting this value of x in equation (I)
x + y = 13
8 + ⬜ = 13
∴ Y = ⬜
The original number is 10
= ⬜ + 8
= 58
A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
Let the digit in unit’s place is x
and that in the ten’s place is y
the number = ⬜y + x
The number obtained by interchanging the digits is ⬜x + y
According to first condition two digit number + the number obtained by interchanging the digits = 143
∴ 10y + x = 143
∴ ⬜x + ⬜y = 143
x + y = ⬜......(I)
From the second condition,
digit in unit’s place = digit in the ten’s place + 3
∴ X = ⬜ + 3
∴ X - Y= 3.....(II)
Adding equations (I) and (II)
2X = ⬜
X = 8
Putting this value of x in equation (I)
x + y = 13
8 + ⬜ = 13
∴ Y = ⬜
The original number is 10
= ⬜ + 8
= 58
Solve : 3x + 2y = 29; 5x - y = 18.
To solve given equations fill the boxes below suitably.
Complete the following table.
Complete the following activity -
Solve the following simultaneous equations by graphical method.
Solve the following simultaneous equation graphically.
5x – 6y + 30 = 0; 5x + 4y – 20 = 0
5x – 6y + 30 = 0; 5x + 4y – 20 = 0
Solve the following simultaneous equation graphically.
x – 3y = 1; 3x – 2y + 4 = 0
x – 3y = 1; 3x – 2y + 4 = 0
Solve the following simultaneous equation graphically.
2x + 3y = 12; x – y = 1
2x + 3y = 12; x – y = 1
Places A and B are 30 km apart and they are on a straight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.
In a factory the ratio of salary of skilled and unskilled workers is 5 : 3. Total salary of one day of both of them is ₹ 720. Find daily wages of skilled and unskilled workers.
Let’s draw graphs of x + y = 4, 2x - y = 2 and observe them
Draw graph of 2x - y = 4.
A three digit number is equal to 17 times the sum of its digits; If the digits are reversed, the new number is 198 more than the old number ; also the sum of extreme digits is less than the middle digit by unity. Find the original number.
Find the value of following determinant:
$\left|\begin{array}{cc}\frac{1}{2} & \frac{-2}{3} \\ \frac{3}{4} & \frac{-4}{5}\end{array}\right|$
View full solution →$\left|\begin{array}{cc}\frac{1}{2} & \frac{-2}{3} \\ \frac{3}{4} & \frac{-4}{5}\end{array}\right|$
Find the value of following determinant:
$\left|\begin{array}{rr}-3 & 8 \\ 6 & 0\end{array}\right|$
View full solution →$\left|\begin{array}{rr}-3 & 8 \\ 6 & 0\end{array}\right|$
Find the value of following determinant:
$\left|\begin{array}{rr}5 & -2 \\ -3 & 1\end{array}\right|$
View full solution →$\left|\begin{array}{rr}5 & -2 \\ -3 & 1\end{array}\right|$
Find the value of following determinant:
$\left|\begin{array}{rr}5 & -2 \\ -3 & 1\end{array}\right|$
View full solution →$\left|\begin{array}{rr}5 & -2 \\ -3 & 1\end{array}\right|$
Find the value of following determinant:
$\left|\begin{array}{rr}-3 & 8 \\ 6 & 0\end{array}\right|$
View full solution →$\left|\begin{array}{rr}-3 & 8 \\ 6 & 0\end{array}\right|$
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