Class 10 Practice – Level 2 – Set 1- Pair Of Linear Equations in Two Variables

Total questions: 25

Solve the system of equations: $ \displaystyle \begin{array}{l}3x+4y=10\\5x-6y=-8.\end{array}$

Topic: Solving Systems of Equations

$ \displaystyle x=2.y=1$

$ \displaystyle x=1,y=1$

$ \displaystyle x=2,y=-1$

$ \displaystyle x=1,y=2$

None

Find the point of intersection of the lines $ \displaystyle 2x-3y=5\text{ and }3x-y=4.$

Topic: Intersection of Lines

(2,1)

(3,2)

(1,-1)

(4,1)

None

The lines $ \displaystyle ax+by=c\text{ and }dx+ey=f$ are parallel if:

Topic: Condition for Parallel Lines

$ \displaystyle \frac{a}{b}=\frac{d}{e}$

$ \displaystyle \frac{a}{d}=\frac{b}{e}$

$ \displaystyle \frac{a}{d}\ne \frac{b}{e}$

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

None

Find the slope of the line perpendicular to the line $ \displaystyle 4x+3y=7.$

Topic: Slope of a Line

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

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

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

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

None

If two lines intersect at a point, the system of equations representing them has:

Topic: Graphical Solutions

No solution

One solution

Two solutions

Infinite solutions

None

Find the distance between the points (1,2) and (4,6).

Topic: Distance Between Point

None

Solve the system of equations using substitution: $ \displaystyle \begin{array}{l}x+2y=7\\2x-3y=4.\end{array}$

Topic: Solving by Substitution

(2,3)

(3,2)

(1,3)

(3,1)

None

A system of equations is consistent if:

Topic: Consistent Systems

It has exactly one solution

It has no solution

It has infinite solutions

It has at least one solution

None

Find the equation of a line with a slope of 2 passing through the point (3,4).

Topic: Equation of a Line

$ \displaystyle y=2x+1$

$ \displaystyle y=2x-2$

$ \displaystyle y=2x+4$

$ \displaystyle y=2x-3$

None

10.

A pair of linear equations has a unique solution if:

Topic: Unique Solutions

The lines are parallel

The lines are coincident

The lines intersect at a point

The slopes are equal

None

11.

The slope of the passing through (1,2) and (3,4) is:

Topic: Slope from Two Point

$ \displaystyle \frac{1}{2}$

$ \displaystyle \frac{2}{3}$

None

12.

Two lines $ \displaystyle ax+by=c\text{ and }dx+ey=f$ are coincident if:

Topic: Condition for Coincident Lines

$ \displaystyle \frac{a}{d}\ne \frac{b}{e}$

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

$ \displaystyle \frac{a}{b}=\frac{d}{e}$

$ \displaystyle \frac{a}{d}=\frac{b}{e}$

None

13.

Find the equation of the line passing through the point (1,2) and (3,4).

Topic: Equation of a Line from Two Points

$ \displaystyle y=x+1$

$ \displaystyle y=2x-2$

$ \displaystyle y=2x+2$

$ \displaystyle y=x+2$

None

14.

Find the equation of a line perpendicular to $ \displaystyle y=\frac{1}{2}x+3$ passing through (2,4).

Topic: Equation of a Line

$ \displaystyle y=-2x+8$

$ \displaystyle y=2x-4$

$ \displaystyle y=-2x+6$

$ \displaystyle y=-2x+4$

None

15.

The system of equations $ \displaystyle 2x-3y=5\text{ and 4}x-6y=10$ has:

Topic: Types of Solutions

One solution

No solution

Infinite solutions

Exactly two solutions

None

16.

The line $ \displaystyle y=-x+2$ intersects the x-axis at:

Topic: Graphical Representation

(2,0)

(1,1)

(0,2)

(-2,2)

None

17.

The slope of the line parallel to $ \displaystyle y=5x-7$ is:

Topic: Finding Slope

-5

$ \displaystyle \frac{1}{5}$

$ \displaystyle -\frac{1}{5}$

None

18.

Which of the following points lies on the line $ \displaystyle 3x+2y=7$?

Topic: Solution Verification

(1,2)

(2,1)

(0,3)

(3,0)

None

19.

Find the equation of a line with a slope $ \displaystyle -1$ passing through ($ \displaystyle 1,-2$).

Topic: Finding Solution

$ \displaystyle y=-x+1$

$ \displaystyle y=-x-1$

$ \displaystyle y=x+2$

$ \displaystyle y=-x-2$

None

20.

Which of the following equations represents a line parallel to $ \displaystyle y=3x+4?$

Topic: Graphing Line

$ \displaystyle y=-3x+4$

$ \displaystyle y=3x-4$

$ \displaystyle y=\frac{1}{3}x+4$

$ \displaystyle y=-\frac{1}{3}x-4$

None

21.

Solve the system of equations using the elimination method: $ \displaystyle \begin{array}{l}2x+3y=6\text{ }\\\text{4}x+6y=12.\end{array}$

Topic: Solving by Elimination

No solution

Infinite solutions

$ \displaystyle x=0,y=2$

$ \displaystyle x=2,y=0$

None

22.

Which of the following points does not lie on the line $ \displaystyle y=2x+3?$

Topic: Solving by Graphing

(1,5)

(0,3)

(-1,1)

(2,7)

None

23.

The x-intercept of the line $ \displaystyle 6x-2y=12\text{ is:}$

Topic: X-Intercept

None

24.

The slope of the line passing through (-2,1) and (1,-5) is:

Topic: Identifying Slope

$ \displaystyle -2$

$ \displaystyle \frac{2}{3}$

$ \displaystyle -\frac{2}{3}$

None

25.

Find the equation of a line with slope 3 and y-intercept 5.

Topic: Equation of a Line

$ \displaystyle y=3x+5$

$ \displaystyle y=5x+3$

$ \displaystyle y=3x-5$

$ \displaystyle y=-3x+5$

None

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Class 10 Practice – Level 2 – Set 1- Pair Of Linear Equations in Two Variables

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