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

Total questions: 25

The lines $ \displaystyle 2x+3y=5$ and $ \displaystyle 4x+6y=10$ are:

Topic: Condition for Intersecting Lines

Parallel

Perpendicular

Intersecting at a point

Coincident

None

The graph of $ \displaystyle y=2x+3$ intersecting the y-axis at:

Topic: Graphical Solutions

(0,3)

(3,0)

(2,0)

(0,2)

None

The solution to the system of equations $ \displaystyle 3x+y=7\text{ and }2x-3y=4$ is:

Topic: System of Equations

(1,4)

(2,1)

(3,2)

(1,2)

None

The lines $ \displaystyle 3x-2y=6\text{ and 6}x-4y=12$ are:

Topic: Condition for Parallel Lines

Parallel

Perpendicular

Intersecting at a point

Coincident

None

Find the equation of the line passing through (2,3) with a slope of $ \displaystyle \frac{1}{2}$.

Topic: Equation of a Line

$ \displaystyle y=\frac{1}{2}x+2$

$ \displaystyle y=\frac{1}{2}x+2.5$

$ \displaystyle y=\frac{1}{2}x+4$

$ \displaystyle y=\frac{1}{2}x+4.5$

None

A system of equations is inconsistent if:

Topic: Identifying Consistent Slope

It has one solution

It has infinite solutions

The lines are parallel

The lines are coincident

None

Solve for $ \displaystyle x\text{ and }y$ using substitution in the system:

Topic: Solving by Substitution

$ \displaystyle \begin{array}{l}x+y=8\text{ }\\2x-y=3.\end{array}$

$ \displaystyle x=4,y=4$

$ \displaystyle x=5,y=3$

$ \displaystyle x=6,y=2$

$ \displaystyle x=3,y=5$

None

The equation of a line perpendicular to $ \displaystyle y=3x+1$ and passing through (2,-3) is:

Topic: Perpendicular Lines

$ \displaystyle y=-\frac{1}{3}x-2$

$ \displaystyle y=-\frac{1}{3}x-\frac{7}{3}$

$ \displaystyle y=-\frac{1}{3}x+\frac{7}{3}$

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

None

If a line has a slope of 5, what is the slope of a line parallel to it?

Topic: Identifying Slope

$ \displaystyle {-5}$

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

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

None

10.

The distance between the points ($ \displaystyle 2,-1$) and ($ \displaystyle -2,3$) is:

Topic: Distance Between Point

None

11.

Find the equation of a line parallel to $ \displaystyle y=-2x+3$ passing through (4,5).

Topic: Equation of a Line

$ \displaystyle y=-2x+7$

$ \displaystyle y=-2x-1$

$ \displaystyle y=-2x+9$

$ \displaystyle y=2x+1$

None

12.

Which of the following equations represents a line with slope 4 and y-intercept -3?

Topic: Slope Intercept Form

$ \displaystyle y=4x+3$

$ \displaystyle y=-4x-3$

$ \displaystyle y=4x-3$

$ \displaystyle y=-4x+3$

None

13.

Find the solution to the system of equations $ \displaystyle x-2y=3\text{ and }2x+3y=6.$

Topic: System of Equations

(3,0)

(0,2)

(2,3)

(1,2)

None

14.

The y-intercept of the line $ \displaystyle 4x-y=8$ is:

Topic: Finding Intercepts

-8

-4

None

15.

The lines $ \displaystyle y=2x+3$ and $ \displaystyle y=-\frac{1}{2}x+1$ intersect at:

Topic: Intersection of Lines

(1,2)

(2,1)

(3,4)

(4,3)

None

16.

If the slope of a line is $ \displaystyle -\frac{3}{4},$ the slope of a line perpendicular to it is:

Topic: Identifying Perpendicular Slope

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

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

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

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

None

17.

The equation of a line perpendicular to $ \displaystyle y=-\frac{1}{2}x+4$ and passing through (2,-3) is:

Topic: Parallel and Perpendicular Lines

$ \displaystyle y=2x-7$

$ \displaystyle y=-2x+7$

$ \displaystyle y=2x+1$

$ \displaystyle y=\frac{1}{2}x+4$

None

18.

Two lines represented by the equations $ \displaystyle 4x+5y=6\text{ and }8x+10y=12\text{ are:}$

Topic: Condition for Coincident Lines

Parallel

Perpendicular

Intersecting at a point

Coincident

None

19.

Solve for $ \displaystyle x\text{ and }y$ in the system of equations:

Topic: Solving by Elimination

$ \displaystyle \begin{array}{l}2x+3y=6\text{ }\\4x-y=7.\end{array}$

$ \displaystyle x=2,y=0$

$ \displaystyle x=1,y=1$

$ \displaystyle x=2,y=2$

$ \displaystyle x=1,y=0$

None

20.

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

Topic: Graphical Solutions

(1,1)

(2,3)

(0,0)

(-1,1)

None

21.

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

Topic: Slope from Point

-3

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

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

None

22.

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

Topic: Equation of a Line

$ \displaystyle y=2x-3$

$ \displaystyle y=2x-1$

$ \displaystyle y=2x+3$

$ \displaystyle y=2x+1$

None

23.

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

Topic: Intersection Point

(1,3)

(3,1)

(2,1)

(1,2)

None

24.

If the slope of a line is $ \displaystyle \frac{2}{3}$, the slope of a line parallel to it is:

Topic: Parallel Slopes

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

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

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

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

None

25.

Solve for $ \displaystyle x$ in the system of equations:

Topic: Solving by Substitution

$ \displaystyle \begin{array}{l}3x+4y=10\\x+2y=4.\end{array}$

$ \displaystyle x=2$

$ \displaystyle x=3$

$ \displaystyle x=1$

$ \displaystyle x=4$

None

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

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