Grade 10 : Mathematics - 3. Linear Equations (Set 1)

Question 1

How many solutions does the system of linear equations $2x + 3y = 7$ and $4x + 6y = 14$ have?

Accepted Answer

B) Infinitely many solutions

Answer

A) Unique solution

Answer

C) No solution

Answer

D) Exactly two solutions

Question 2

For what value of $k$ will the system of equations $x + 2y = 3$ and $5x + ky = 7$ have no solution?

Accepted Answer

C) $k = 10$

Answer

A) $k = 5$

Answer

B) $k = 2$

Answer

D) $k = 15$

Question 3

What is the solution to the system of linear equations $x + y = 10$ and $x - y = 4$?

Accepted Answer

A) $x = 7, y = 3$

Answer

B) $x = 6, y = 4$

Answer

C) $x = 8, y = 2$

Answer

D) $x = 5, y = 5$

Question 4

Which of the following ordered pairs is a valid solution to the equation $3x - 2y = 5$?

Accepted Answer

B) $(3, 2)$

Answer

A) $(2, 1)$

Answer

C) $(1, 2)$

Answer

D) $(4, 2)$

Question 5

At what point does the straight line $2x + 5y = 10$ intersect the x-axis?

Accepted Answer

C) $(5, 0)$

Answer

A) $(0, 2)$

Answer

B) $(0, 5)$

Answer

D) $(2, 0)$

Question 6

Find the coordinates of the point where the line $4x - 3y = 12$ crosses the y-axis.

Accepted Answer

A) $(0, -4)$

Answer

B) $(-4, 0)$

Answer

C) $(0, 4)$

Answer

D) $(3, 0)$

Question 7

A pair of linear equations in two variables that has infinitely many solutions is classified as:

Accepted Answer

B) Dependent and consistent

Answer

A) Inconsistent

Answer

C) Independent and consistent

Answer

D) Inconsistent and dependent

Question 8

The sum of two numbers is 25 and their difference is 7. What are the two numbers?

Accepted Answer

D) 16 and 9

Answer

A) 15 and 10

Answer

B) 14 and 11

Answer

C) 18 and 7

Question 9

The perimeter of a rectangular field is 30 m. If its length is 3 m more than its width, what is its length?

Accepted Answer

B) 9 m

Answer

A) 6 m

Answer

C) 12 m

Answer

D) 15 m

Question 10

If $3x + y = 4$ and $9x + 3y = c$ represent coincident lines, what is the value of $c$?

Accepted Answer

A) 12

Answer

B) 4

Answer

C) 3

Answer

D) 36

Question 11

For what condition on $k$ does the system $kx - y = 2$ and $6x - 2y = 3$ have a unique solution?

Accepted Answer

C) $k 
eq 3$

Answer

A) $k = 3$

Answer

B) $k = 6$

Answer

D) $k 
eq 6$

Question 12

$x$	1	2	3	4
$y$	3	5	?	9

The table above shows values following the linear equation $y = 2x + 1$. What is the missing value when $x = 3$?

Accepted Answer

B) 7

Answer

A) 6

Answer

C) 8

Answer

D) 7.5

Question 13

A mother is 3 times as old as her daughter. The sum of their present ages is 48 years.

Based on the scenario above, how old is the daughter?

Accepted Answer

A) 12 years

Answer

B) 14 years

Answer

C) 16 years

Answer

D) 36 years

Question 14

Graphically, a system of two linear equations in two variables that has no solution represents:

Accepted Answer

C) Parallel lines

Answer

A) Intersecting lines

Answer

B) Coincident lines

Answer

D) Perpendicular lines only

Question 15

If $x = 3$ is a solution to $2x + y = 11$, what is the value of $y$?

Accepted Answer

D) 5

Answer

A) 3

Answer

B) 4

Answer

C) 6

Question 16

If two linear equations intersect at the point $(2, -3)$, what is the solution of the system?

Accepted Answer

A) $x = 2, y = -3$

Answer

B) $x = -3, y = 2$

Answer

C) $x = -2, y = 3$

Answer

D) $x = 5, y = -1$

Question 17

Express the linear equation $2x + 3y = 6$ in slope-intercept form ($y = mx + c$).

Accepted Answer

B) $y = -\frac{2}{3}x + 2$

Answer

A) $y = \frac{2}{3}x + 2$

Answer

C) $y = -\frac{3}{2}x + 2$

Answer

D) $y = 2x - 6$

Question 18

The cost of 2 pens and 3 notebooks is $40, while 4 pens and 3 notebooks cost $50. What is the cost of 1 pen?

Accepted Answer

C) $5.00

Answer

A) $2.50

Answer

B) $3.00

Answer

D) $10.00

Question 19

Statement I: A linear equation in two variables $ax + by + c = 0$ represents a straight line on a Cartesian plane.
Statement II: Every ordered pair $(x, y)$ satisfying the equation corresponds to a point lying on that line.

Which of the following statements is correct?

Accepted Answer

A) Both Statement I and Statement II are true.

Answer

B) Statement I is true, but Statement II is false.

Answer

C) Statement I is false, but Statement II is true.

Answer

D) Both Statement I and Statement II are false.

Question 20

If $x = a$ and $y = b$ is the solution of $x - y = 2$ and $x + y = 4$, then what are the values of $a$ and $b$?

Accepted Answer

C) $a = 3, b = 1$

Answer

A) $a = 2, b = 2$

Answer

B) $a = 1, b = 3$

Answer

D) $a = 4, b = 0$

Grade 10 : Mathematics - 3. Linear Equations (Set 1)