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Published on: 05/03/2019
Linear Equations in Two Variables Important Questions
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Take MCQ Mathematics Test
1.
The cost of a pen is Rs. 16. Taking number of pens bought as x and total cost as y, form a linear equation in x and y and draw its graph. Find the cost of 6 pens from the graph.
2.
Give the equation of a line passing through (2,14). How many more such lines are there? Write the equation in the form ax+by+c=0.
3.
Give the equations of two lines passing through (-3, 4). How many more such lines are possible?
4.
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-5y
5.
Ram is sitting on a chair in a corner of a huge park. His son Ravi is a student of class X. Mr. Ram asks him, "Draw a straight line passing through my feet him, "Draw a straight line passing through my feet and the centre of the park in 2 minutes. Ravi do so.
(i) Find the co-ordinate of the feet of Mr. Ram if the y-coordinate of the feet is -19.5 and the equation of the line x+y=0
(ii) Find the co-ordinate of the feet of mR. Ram if the y-coordinate of the feet is 20.5 and the equation of the line is x=y.
(iii) Which mathematical concept is used in the above problem?
(iv) Which values do you learn from Ravi?
6.
For the linear equation 3x-5y-15=0, find the points where its graph intersecs x and y axis. Using these, draw the graph of the equation. And find its area.
7.
Write the equation of lines p and r in the given graph.
A student answered the equation of a line 'q' as x+y=1. Did he answered correctly? Also, find the area of lines enclosed between p,q and r.
8.
If x is the number of hours a labourer is on work and y his wages in rupees then y = 4x + 3. Draw the work wages graph of this equation. From the graph, find the wages of a labourer who puts in 4 hours of work
9.
Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively.Age of father 5 years ago was two years ago was teo years more than 7 times the age of his son at that time.
10.
Find the value of K so that x=-1 and y=-1 is a solution of the linear equation 9kx+12ky=63.
11.
Find the co-ordinate of points where the graph of the equation 4x+3y=12 intersects x-axis and y-axis
12.
A part of monthly expense of a family on milk is fixed which is Rs 700 and the remaining varies with the quantity of milk taken extra at the rate of Rs 25 per litre. taking the quantity of milk required extra as x litre and total expenditure on milk is rs y. Write a linear equation representing the above information.
13.
Give the geometric interpretation of 7x + 6 = 2x - 4 as an equation:
(i) in one variable
(ii) in two variables
14.
Solve 4x - 7 = 9. Represent the solution
(i) on the number line
(ii) in the Cartesian plane.
15.
The taxi fare in a city is as follows: for the first kilometer, the fare is Rs.10 and for the subsequent distance it is Rs.6 per km. Taking the distance covered as x km and total fare as Rs.y, write a linear equation for this information, and draw its graph.
16.
Draw the graph of the linear equation 3x + 2y = 12.Also find the points where this graph cuts x-axis and y-axis.
17.
Draw the graph of x + y = 7.
18.
Write the following equations in the form ax+by+c=0 and indicate the values of a, b and c
4=5x-3y
19.
Write the following as an equation in two variables:
2x=3
20.
The value of y at x=-1 in the equation 5y=2 is:
\(5\over 2\)
\(2\over 5\)
10
0
21.
Graph of linear equation 2x+by+c=0, a≠0, b≠0 cuts x-axis and y-axis respectively at the points:
\(\left(-{c\over a},0\right)\left(0,-{c\over b}\right)\)
\(\left(0,-{c\over b}\right),\left(-{c\over a},0\right)\)
(-c, 0),(0, -c)
(x,0), (y,0)
22.
Any point of the form (q, -q) always lie on the graph of the equation:
x=-a
y=a
y=x
x+y=0
23.
Which one of the following graphs represents the graph of x + y = 0?
.png)
.png)
.png)
.png)
24.
In the figure, l is the graph of the equation:
y=x
x+y=0
x=2y
y=2x
25.
The equation whose graph is
x+y=6
x+y=3
x+y+3=0
x+y=0
26.
The maximum number of points that lie on the graph of a linear equation in two variables is:
two
infinite
three
None of these
27.
If x=1, then the value of y from the equation \({4\over x}+{3\over y}=5\) is
1
\(1\over3\)
3
-3
28.
Solution of linear equation 2x+0y+9=0 is:
\(\left(-{9\over 2}, m\right)\)
\(\left(n,-{9\over 2}\right)\)
\(\left(0,-{9\over 2}, \right)\)
\(\left(-{9\over2}, 0\right)\)
29.
The pair satisfying 2x+y=6 is
(1,2)
(2,1)
(2,2)
(1,1)
30.
The line y=x passes through
(0,0)
(0,1)
(1,0)
91,-1)
31.
The salary of Dr.Harikisham is thrice the salary of Manish Goyal.Write a linear equation in two variables to represent the statement.
x=3
x+3y=0
x=3y+3
x=y+3
32.
which of the following is a linear equation?
x2+4x-3=-(x2-1)
x2=3x+4
x+\(1\over x\)=5
(x-1)=1-x
33.
Write a, b, c for the equation 3y+4=0
0,3,4
3,0,4
4,0,3
4,3,0
34.
The equation \(x+\sqrt{2}=0\) has
no solution
infinitely many solutions
only one solution
only two solution
1.
Total cost= value of pen X number of pens
\(\therefore\)y=16x ... (i)
Table of value of (i) is
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | 0 | 16 | 32 | 48 | 64 | 80 | 96 |
From the graph, cost of 6 pens =Rs 96
2.
The line passing through (2,14) is
2y=14x
or y=7x
Infinitely many lines are there
The equation in the form ax+by+c=0 is
7x-y+0=0
3.
x+y+1=0, 2x+x=2, 3y+x=9; infinitely many
4.
2x=-5y
2x+5y+0=0
Comparing with ax+by+c=0, we get
a=2, b=5, c=0
5.
(i) According to the questions, the eqiuation of line is
x+y=0..(i)
The line passes through a point whose y-coordinate is -19.5
y=-19.5
Put the value of y in equation (i), we get
x-19.5=0
x=19.5
So the required coordinates are (19.5-19.5)
(ii) According to the question, the equation of line is
x=y...(ii)
The line passes through a point whose x-coordinate is 20.5
x=20.5
Put this value of x in (i), we get
y=20.5
So the required coordinates are(20.5,20.5)
(iii) The coordinates of all the points lying on a line satisfy the equation of the line.
(iv) Obedience and respect for elders or parents.
6.
3x-5y-15=0
Substituting y=0 in the equation
3x-0-15=0
x=5
Hence the point on x-axis is (5,0)
When x=0 in the equation, we get
(3X0)-5y-15=0
y=-3
Point on y-axis is (0,-3), we get the triangle AOB.
Since OA=5 units and AB=3 units
Area of triangle AOB
\(=\frac{1}{2}\times OA\times OB\)
\(=\frac{1}{2}\times 5\times 3=7.5\) sq.unit.
7.
Equation of p is x=-1
Equation of r is y=-2
Yes, the equation of q is
x+y=1
Area \(=\frac{1}{2}\times4\times 4=8\) sq.units
8.
We have
y=4x+3
Table of solution
| x | 0 | 1 |
|---|---|---|
| y | 3 | 7 |
We plot the points (0,3) and (1, 7) on a graph paper and join the same by a ruler to get the line, which is the graph of the equation y = 4x + 3.
This gives the work wages graph of the given equation.
Now, on x-axis, take a point P(4, 0). From P draw a line parallel to y-axis intersecting the work wage graph at Q. From Q, draw a line parallel to x-axis to intersect the y-axis at R. We see that R is (0, 19).
Hence, the wages of a laborer who puts in 4 hours of work is Rs.19.
9.
Let the present ages of father and son be x years and y year respectively.
Then, Age of father 5 years ago =(x-5)years
Age of his son 5 years ago(y-5) years
According to the question,
x-5=7(y-5)+2
x-y=7y-35+2
x-7y+28=0
which is the required linear equation in two variables.
10.
Substituting x=-1 and y=-1 in 9kx+12ky=63, we get
\(\Rightarrow\) 9k(-1)+12k(-1)=63
\(\Rightarrow\) -9k-12k=63
\(\Rightarrow\) -21k=63 k=-3
11.
Equation 4x+3y=12
For intersection with x-axis
y=0
4x=12
x=3
Co-ordinates are (3,0)
For intersection with y-axis
x=0
3y=12
Co-ordinates are (0,4)
12.
According to equation,
700+25x=y
25x-y+700=0
13.
x=-2
14.
x=4
15.
y=10+6(x-1) ⇒ y=4+6x
16.
(4,0); (0,6)
17.
18.
-5x+3y+4=0; a=-5, b=3 and c=4
or
5x-3y-4=0; a=5, b=-3 and c=-4
19.
2x+0y-3=0
20.
5y = 2 ⇒ \(y={2\over 5}\)
21.
\(ax+b(0)+c=0 \ \ \ \Rightarrow\ \ \ x=-{c\over a}\)
\(a(0)+by+c=0\ \ \ \Rightarrow\ \ \ y=-{c\over b}\)
22.
a+(-a)=0
23.
(-1,1) satisfies y=x+y=0
24.
(2,2) and (-3,-3) both satisfy y=x
25.
(3, 0) satisfies x+y=3
26.
For each value of x, we get the corresponding value of y.
27.
\({4\over1}+{3\over y}=5\ \ \ \Rightarrow\ \ y=3\)
28.
\(\left(-{9\over2},m\right)\) satisfies 2x+0y+9=0 for all values of m.
29.
2(2)+2=6
30.
O(0,0) satisfies y=x
31.
(a)
x=3
32.
x-1=1-x ⇒ x=1 so a linear equation
33.
0x+3y+4=0
34.
(c)
only one solution
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