Solving Simultaneous Linear Equations by Graphical Method

Q.

What is a unique solution in a linear equation?

Q. Question 12
Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y - axis, find the area of this triangle?

Q.

Equation to the straight line cutting off an intercept $2$ from the negative direction of the axis of $y$ and inclined at $30°$ to the positive direction of axis of$x$, is

1. $y+x–\surd 3=0$

2. $y–x+2=0$

3. $y–\surd 3x–2=0$

4. $\surd 3y–x+2\surd 3=0$

Q.

Solve the equations x+2y=4 and 3x-y=5 by graphical method.

1. (2, 3)
2. (2, 1)
3. (2, 5)
4. (3, 1)

Q.

The ratio of $25$ minutes to $1$ hour is

Q. A linear equation in two variables ___.

1. has no solution
2. has one solution
3. has infinitely many solutions
4. has two solutions

Q.

The pair of equations $x+2y+5=0$ and $-3x-6y+1=0$ have,

1. A unique solution

2. Exactly two solutions

3. Infinitely many solutions

4. no solution

Q.

If the lines of regression of $y$ on $x$ and $x$ on $y$ make angles $30°$ and $60°$ respectively with the positive direction of the $x-$axis, then the correlation coefficient between $x$ and $y$ is

1. $\frac{1}{\sqrt{2}}$

2. $\frac{1}{2}$

3. $\frac{1}{\sqrt{3}}$

4. $\frac{1}{3}$

Q.

Simplify: $3(n-4)+2(4n-5)=5(n+2)+16$

Q.

Give the equation of two lines passing through $(2,10)$.

Q.

Find the ratio of $18$ seconds to $1$hours.

Q.

Suppose 2 kg of sugar contains $9\times {10}^6$ crystals.

How many sugar crystals are there in

(i) 5 kg of sugar?

(ii) 1.2 kg of sugar? [2 MARKS]

Q. write the condition for no solution and infinite solutions for two lines.

Q. $\mathrm{The}\mathrm{lines}2x+y-6=0,4x-2y-4=0\mathrm{are}$

1. Intersecting at single point
2. Intersecting at multiple points
3. Parallel lines
4. None of the above

Q.

Draw the graph of the equations $2x-y+6=0$ and $2x+y-6=0$. Also determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.

Q.

For what condition does the pair of equations −3x + py + 10 = 0 and 4x + 4y + 17 = 0 represents a pair of intersecting lines?

1. 

2. 

3. 

4. 

Q.

A rectangle measures $40cm$ its length and $20cm$ at its width. Find the ratio of the length to the width??

Q.

Which of these linear equations is written in slope-intercept form?

1. y = 3x + 2

2. 3x + 2y = 6

3. 6 + y = x

4. y + x = 1

Q. Question 11 (ii)
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.
X – 2y = 6, 3x – 6y = 0

Q.

Find the solution of the pair of linear equations
$x+2y=5$ and $7x+3y=13.$

1. (1, 2)

2. (2, 1)

3. (3, 1)

4. (1, 3)

Q. Question 6
Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Q. In winters, a school opens at $10$a.m and closes at $3.30$p.m.If the lunch interval is of $30$ minutes, find the ratio of lunch interval to total time of the class periods.

Q. Find the value of $k$ so that the line $x+5ky-3=0$ may be parallel to $x+y-6=0$

Q. Solve the following pair of equations graphically.
$2x-3y-6=0;2x+y+10=0$

Q.

The equation of the line shown in the figure is

1. x = 1

2. y = 1

3. y = 0

4. x = 0

Q. Scooter charges consist of fixed charges and the remaining depending upon the distance traveled in kilometers. If a person travels $12km,$ he pays Rs. 45 and for travelling 20 $km,$ he pays Rs. $73.$ Express the above statements in the form of simultaneous equations and hence, find the fixed charges and the rate per km.

Q. Find the value of $k$ so that the line $3x-ky-1=0$ may be perpendicular to $4x-y-3=0$

Q.

two rails are represented by the equations x+2y-4=0 and 2x+4y-12=0. solve it algebrically and will the rails cross each other?

Q.

The equation of every line on the XY plane will require both x and y variables

1. True

2. False

Q. Find the value of $k$ so that the line $kx-6y-3=0$ may be parallel to $x-ky+5=0$.