9th Standard CBSE Mathematics - Linear Equations in Two Variables Three Marks Questions | QB365

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9th Standard CBSE Mathematics - Linear Equations in Two Variables Three Marks Questions

Published on: 21/09/2019

Linear Equations in Two Variables

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Std: 9th Standard CBSE - Mathematics

chapter: - Model Question paper

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Questions:

Generic 3

14 x 3 = 42

Write the equation \(\frac{x}{2}+\frac{3y}{5}=-1\) in standard form and draw the graph.

Write three solutions of the equation 3x=y+3. Draw its graph and find the points where the graph intersects the axes.

Find two different solutions of the equation 4x+3y=12 from its graph.

Given the equation 2x+y=7
(i) What is the value of x, when the value of y is 3?
(ii) What is the value of y, when the value of x is 4?
(iii) Find one more solution for the above equation.

If the point (-1,-5) lies on the graph of 3x=ay+7, then find the value of 'a'.

The cost a notebook in a book-shop is Rs.15.Form a linear equation with x-representing the number of notebooks and y-representing the total cost (in Rs) and draw its graph.From the graph, find the total cost if 5 notebooks are purchased

Write \(\sqrt{7}y=2x\)as a linear equation of the form ax+by+c=0.Also write the values corresponding to a, b, c.Does the graph of this linear equation pass through origin?Give your answer in yes or no.

Give the equations of two lines passing through (-3, 4). How many more such lines are possible?

Yamini and Fatima, two students of Class IX of a school, together contributed Rs.100 towards the Prime Minister's Relief Fund to help the earthquake victims.Write a linear equation which satisfies this data. (You may take their contributions as Rs.x and Rs.y) Draw the graph of the same.

10.

Draw the graph of the following linear equations in two variables:
y=3x

11.

Check which of the following are solutions of equation x-2y = 4 and which are not:
(2,0)

12.

Which one of the following options is true and why?
y = 3x + 5 hs
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions

13.

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
-2x+3y=6

14.

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
\(x-{y\over 5}-10=0\)

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Answers Key:

Generic 3

14 x 3 = 42

The equation can be written as,
5x+6y=-10
\(\Rightarrow -y=(5x+10)/6\)

x	-3	4	10
y	0	-5	-10

3x=y+3; three solutions are x=1, y=0; x=2, y=3 and x=0, y=-3

From graph it is clear that line meets x-axis at(1,0) and y-axis at (0,-3)

Given equation
4x+3y=12
Put x=0, the 0+3y=12
y=4
hence point on y-axis is (0,4)
Now put y=0, then
4x+0=12
x=3
Hence point on x-axis is (3,0)

(i) when y=3, then
2x+3=7
\(\Rightarrow\)2x=4
\(\Rightarrow\)x-=2
(ii)when x=4, then
2(4)+y=7
\(\Rightarrow\) y=7-8=-1
(iii) when x=1, then
2+y=7\(\Rightarrow\) y=5
\(\therefore \)One more solution is (1,5)

(-1,-5) lies on the graph of
3x=ay+7
3(-1)=aX(-5)+7
\(\Rightarrow\)-3=-5a+7\(\Rightarrow\) 5a=10
\(\Rightarrow\)a=2

y=15x, Rs.75

\(2x-\sqrt{7}+0=0;\ a=2,\ b=-\sqrt{7}.,\ c=0\) Yes.

x+y+1=0, 2x+x=2, 3y+x=9; infinitely many

Let the contributions ofYarnini and Fatima be Rs.x and Rs.y respectively.
Then according to the question
x + y = 100
This is the linear equation which the given data satisfies.
Now, x + y = 100
⇒ y = 100-x
Table of solution

X	0	50
Y	100	50

We plot the points (0, 100) and (50, 50) on the graph paper and join the same by a ruler to get the line which is the graph of the equation x + y = 100.