Class 10 Practice – Level 3 – Set 1- Pair Of Linear Equations in Two Variables

Total questions: 15

Solve the system of equations:

Topic: Solving Non-Linear Equations

$ \displaystyle x+2y=10$
$ \displaystyle x+y=4$

(2, 2)

(-2, 6)

(6, 2)

(2, 3)

None

The system of equation 2𝑥 + 3y = 5 and 4𝑥 + 6y = k, will have infinite solution if :

Topic: Condition for Infinite Solutions

k = 5

k = 10

k = 0

k = 15

None

Solve the system of equations:

Topic: System of Non-Linear Equations

$ \displaystyle y=x+1$
$ \displaystyle x+y=9$

(3, 10)

(4, 5)

(2, 5)

(1, 2)

None

The lines 3𝑥 + 4y = 7 and a𝑥 - 3y = 5 are perpendicular if :

Topic: Condition for Perpendicular Lines

$ \displaystyle a=\frac{4}{3}$

a = -4

a = 4

$ \displaystyle a=-\frac{4}{3}$

None

Find the point of intersection for the equations $ \displaystyle 2x+y=10$ and $ \displaystyle x+y=7$ .

Topic: Intersection of Non-Linear Equation

(3, 4)

(5, 2)

(4, 3)

(2, 5)

None

The lines a𝑥 + by = cand d𝑥 +cy = f are coincident if:

Topic: Condition for Coincident Lines

$ \displaystyle \frac{a}{d}=\frac{b}{c}\ne \frac{c}{f}$

$ \displaystyle \frac{a}{d}\ne \frac{b}{c}\ne \frac{c}{f}$

$ \displaystyle \frac{a}{d}=\frac{b}{c}=\frac{c}{f}$

$ \displaystyle \frac{a}{d}\ne \frac{b}{c}=\frac{c}{f}$

None

Solve the system 2𝑥 + y = 3 and $ \displaystyle x + y=5$ .

Topic: Solving by Substitution

(-2, 7)

(2, -1)

(-1, 5)

(0, 3)

None

The system of equation $ \displaystyle x + y=16$ and y = 𝑥 + 4 has :

Topic: Analyzing Equation

One solution

Two solution

No solution

infinite solution

None

Find the points of intersection for the equation $ \displaystyle 4x+y=4$ and 2𝑥 - y =2.

Topic: Intersection of Curves

(2, 2)

(3, 4)

(4, 8)

(1, 0)

None

10.

The lines 5𝑥 + 2y = 7 and a𝑥 - 10y = 5 are perpendicular if:

Topic: Condition for Perpendicular Lines

a = -4

a = 4

$ \displaystyle a=-\frac{5}{2}$

$ \displaystyle a=\frac{5}{2}$

None

11.

Solve the system of equation:

Topic: Non-Linear Systems

$\displaystyle x-y=13$
$ \displaystyle x+y=3$

(8, 8)

(1, 2)

(-2, 5)

(8, 0)

None

12.

Find the real solution to the systems:

Topic: Complex Systems

$ \displaystyle x - y=4$
$ \displaystyle x+y=4$

(2, 4)

(3, 1)

(2, 2)

(4, 0)

None

13.

The system of equations 3𝑥 +4y = 7 and 6𝑥 + 8y = k has infinitely many solutions if:

Topic: Multiple Solution

K = 7

K = 14

k = 21

k = 10

None

14.

The system of equations $ \displaystyle x + y=25$ and 𝑥 -y = 7 has:

Topic: Analyzing Equation

One solution

Two solution

No solution

Infinite solutions

None

15.

Find the points of intersection for the system:

Topic: System Involving Quadratics

$ \displaystyle y=-6x+9$
$\displaystyle y=2x-1$

(-1, 3)

(2, 3)

(4, 7)

(1, 1)

None

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Class 10 Practice – Level 3 – Set 1- Pair Of Linear Equations in Two Variables

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