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The chapter-4 Linear Equations in Two Variables follows the operations performed on the Linear Equations in One Variables extended to another variable. This chapter also discusses the representation of the solution. Further, this chapter discusses whether or not a Linear Equation in Two variables has a solution or not, if it does then whether it is unique or not and how it can be represented on a cartesian plane.
The Class 9 Maths Linear Equations in Two variables along with Polynomials has 7 questions in for 20 marks in total. This article discusses a few MCQs related to The Class 9 Maths Linear Equations in Two variables.
Also Read: Linear Equation in Two Variables
Question: The linear equation 6x-12y=0 has
- Unique solution
- Two solutions
- Infinite solutions
- No solution
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Answer: c. Infinite solutions
Explanation:
6x-12y=0
6x=12y
y=6x/12
For infinite values x and y also have infinite solutions.
Question: The solution of equation 8x-2y=4 is
- (0,3)
- (0,2)
- (1,2)
- (2,1)
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Answer: c. (1,2)
Explanation:
8x-2y=4
When x=1, y=2 on L.H.S
8(1)-2(2)
= 8-4
= 4
That is equal to R.H.S
Hence solution is (1,2)
Question: Find the value of m, if x=3, y=6 is the solution for equation x+2y=m?
- 10
- 15
- 12
- 14
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Answer: b. 15
Explanation:
Given equation is x+2y=m
If x=3 and y=6 then
3+2(6)=m
3+12=m
m=15
Question: The graph of linear equation 6x-2y=8 cuts the y-axis at
- (0,-4)
- (0,4)
- (0,2)
- (0,-2)
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Answer: a. (0,-4)
Explanation:
Given equation 6x-2y= 8
6x-8=2y
y=(6x-8)/2
Since the equation cuts y-axis, x=0
Then y=(6(0)-8)/2
y= (-8)/2
y= -4
Hence, 6x-2y=8 cuts the y-axis at (0,-4).
Question: The graph y=4 is a line
- Parallel to X-axis at a distance of 4 units from origin.
- Parallel to Y-axis at a distance of 4 units from origin.
- Makes an intercept 4 on X-axis
- Makes an intercept 4 on Y-axis
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Answer: a. Parallel to X-axis at a distance of 4 units from origin
Question: If x and y solutions for equation ax+by=c are negative and positive, the line lies in the:
- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
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Answer: b. Second Quadrant
Explanation:
The second quadrant consists of Negative X-axis and Positive Y-axis.
So, second quadrant has (-,+) values.
Question: Any point on Y-axis is of the form
- (x,y)
- (y,x)
- (0,y)
- (y,0)
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Answer: c
Explanation:
When a point lies on the Y-axis it consists only of Y value. It doesn’t have a value on the X-axis. So, the point on the Y-axis is of the form (0,y).
Question: The point (3,3) lies on
- On the line x+y=0
- On the X-axis
- On the line x=y
- On the Y-axis
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Answer: c
Explanation:
Given (3,3)
The point has the same x and y values. When a point has the same x and y values in the form of (a,a) then the point lies on the same line.
Hence, (3,3) lies on the line x=y.
Question: When the equation is multiplied or divided by a same non-zero number on both sides, the solution of the equation
- Remains same
- Increases
- Changes when multiplied only
- Changes when divided only
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Answer: a
Explanation:
If an equation is either multiplied or divided by a same non-zero number on both sides, it does not affect the solution. The solution of the equation remains the same.
Question: Find the number of solutions for the pair of linear equations x+3y=9 and 8x+16y=32.
- 1
- 2
- 0
- Infinite
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Answer: d. infinite
Explanation:
Given equations
x+3y=9. 8x+16y=32
x-9=3y. 8x-32=16y
y=(x-9)/3. y=(8x-32)/16
Here for various values of x we get various values of y. Infinite values can be considered in the place of x and y.
So, these Equations have infinite solutions.
Also Check: Pair of Linear Equations in Two Variables Revision Notes
Question: If the solution is x=2 and y=3 then the linear equation is
- 2x+6y=14
- x+5y=17
- 2x+5y=17
- x+y=7
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Answer: b
Explanation:
Given x=2 and y=3
Substituting in b
x+5y=17
2+5(3)=17
2+15=17
17=17
Hence, L.H.S = R.H.S
So, the equation is x+5y=17
Question: The standard form of linear equation in two variables is
- ax+by=c
- ay+b=0
- ax+by+c=0
- ax+by+xy=0
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Answer: c. ax+by+c=0
Explanation:
The linear equation with two variables x and y will always be of the form
ax+by+c=0
Question: The degree of a linear equation is
- 1
- 2
- 3
- 0
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Answer: a
Explanation:
The equation with degree 1 is called as Linear equation. Here degree is the highest power of a variable in the equation.
Question: The slope of X and Y axis are
- 0 and undefined
- Undefined and 0
- Infinity
- 0 and 0
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Answer: a
Explanation:
A line parallel to X-axis or the X-axis has no slope. So, slope of X-axis is 0.
A line parallel to Y-axis or the Y-axis has no defined slope. So, slope of Y-axis is undefined.
Question: The slope of the linear equation ax+by+c=0 is
- m=a/b
- m=-a/b
- m=-b/a
- m=b/a
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Answer: b. m=-a/b
Explanation:
Slope intercept form is y=mx+c. Here m is the slope of equation.
ax+by+c=0 can be written as by=-ax-c
y=(-a/b)x-c/b
It is in the form y=mx+c
So, the slope m=-a/b
Question: If x=4 and y=-2 are the solution for the equation 4px+2y=12 Then the value of p is
- 1
- 2
- 3
- 4
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Answer: a. 1
Explanation:
Given equation 4px+2y=12
Here x=4 and y=-2
Substituting x and y in equation
4p(4)+2(-2)=12
16p-4=12
16p=12+4
16p=16
P=1
Hence the value of p is 1.
Question: The point for the equation y=4x is
- (2,4)
- (1,4)
- (3,4)
- None
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Answer: b. (1,4)
Explanation:
Given equation y=4x
When x=1, then y=4(1)=4.
So, when y=ax then the point is of the form (x,ax).
Question: The cost of a pen(x) is ten more than thrice the cost of book(y). It can be expressed in the form of linear equation as
- x+3y-10=0
- x-3y-10=0
- x+3y+10=0
- x-10(3y)=0
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Answer: b. x-3y-10=0
Explanation:
Given cost of a pen=x
Cost of book=y
Thrice the cost of book is 3*y= 3y
Ten more than thrice the cost of book is 10+3y
So, the cost of pen is ten more than thrice the cost of book
x=3y+10
x-3y-10 is the equation.
Question: The straight line passing through the points (0,0), (-2,2) and (2,-2) is
- x-y=0
- y=x
- x+y=0
- x+2y=0
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Answer: c. x+y=0
Explanation:
Substitute all the values in Equations and check the R.H.S and L.H.S
x+y=0
(0,0) 0+0=0
(-2,2) -2+2=0
(2,-2) 2-2=0
This equation is equal to zero for all the points.
So, the equation of line is x+y=0
Question: The values of a and b in a linear equation ax+by+c=0 are
- a=0 and b=0
- a≠0 and b≠ 0
- a ≠ 0 and b=0
- a= 1 and b=0
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Answer: b. a≠0 and b≠ 0
Explanation:
The co efficient values of x and y are a and b.
These values of a and b are always not equal to zero.
This is a condition for the linear equation.
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