10th Grade > Mathematics
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES MCQs
:
B and D
The given equation is
3x=2y−2.
After rearranging the equation, we get
⇒3x−2y+2=0
On comparing the above equation with ax+by+c=0, we get
a = 3, b = -2 and c = 2
∴ The values of a, b and c are 3, -2 and 2 respectively.
But the equation can also be written as
(−1)×(3x−2y+2)=(−1)×0
⇒−3x+2y−2=0
On comparing the above equation with ax+by+c=0, we get
a = -3, b = 2 and c = -2
∴ The values of a, b and c are -3, +2 and -2 respectively.
Hence, we have two sets of values for a, b and c.
:
A
The line intersects the y axis when the value of x coordinate is 0.
Thus, on y axis, x=0.
Substituting this value in the given equation:
⇒5y=10
⇒y=2
Thus, the line intersects the y axis at point (0,2).
:
A
Let the 2 parts of 54 be x and y
x+y = 54 ....(i)
and 10x + 22y = 780 ...(ii)
Multiply (i) by 10 , we get
10 x + 10 y = 540 ...(iii)
Subtracting (ii) from (iii)
- 12y = - 240
y = 20
Subsituting y = 20 in x + y = 54 ,
⟹ x + 20 = 54
⟹x = 34
Hence, x = 34 and y = 20
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C
Let the measure of the angle be x and that of its adjacent angle be y.
x=2y ...(i) (given)
x+y=180∘ ...(ii)
(sum of adjacent angles of a parallelogram is 180∘)
On substituting (i) in (ii), we get
2y+y=180∘
⇒y=60∘
Since x=2y, x=120∘.
We know that opposite angles of parallelogram are equal.
⇒ Measure of the angles are 60∘, 120∘, 60∘ and 120∘.
:
B
A pair of linear equations in two variables which has a solution, is said to be consistent.
Here the lines representing the given linear equations are meeting only at point (-2, 3.5) giving a unique solution. Therefore, it is a consistent pair of linear equations.
Now, a pair of linear equations in two variables is said to be dependent when the lines representing them are coinciding i.e. will have many solutions.
Here, the lines have only one solution (-2, 3.5). Therefore, they aren't dependent.
:
Let, p = 12+x and q = 1y−4
Thus, given equations reduce to,
5p+q=2 ... (i)
6p−3q=1 ... (ii)
On multiplying (i) by 3 and then adding it to (ii), we get
15p+3q=6
6p−3q=1
_______________
21p=7
⇒p=13
and on substituting this value in (ii) we get
613−3q=1
⇒q=13
Now, p=12+x
⇒13=12+x
⇒x=1
We know that q=1y−4
⇒13=1y−4
⇒y=7
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B
Let the line intersects at point (x, y).
We know that if a line intersects the x-axis then the y coordinate of the point at which it intersects will be 0.
⇒ y = 0
On substituting y = 0 in the given equation, we get
6x+0=9
⇒x=32
Thus, the point at which the given line intersects the x-axis is (32,0).
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D
We have y−3x+1=0
For x=3
⇒y−3(3)+1=0
∴y=8
For x=−4
⇒y−3(−4)+1=0
∴y=−13
For x=2
⇒y−3(2)+1=0
∴y=5
Thus, the values of y if x=[3,−4,2] are 8, -13 and 5 respectively.
:
B
Two linear equations in same two variables are called pair of linear equation in two variables.
12x+4y+3=0 and 4x+4y+4=0
are linear equations in same two variables.
:
A
The standard form of a linear equation is ax+by+c=0.
The given equation is y=7x−4.
It can be rewritten as −7x+y+4=0.
⇒a=−7,b=1 and c=4.
But the equation can also be written as,
7x−y−4=0.
⇒a=+7,b=−1 and c=−4.