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Published on: 14/09/2019
Linear Equations in Two Variables
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Questions + Answers key
Take MCQ Mathematics Test
1.
Find the value of K so that x=-1 and y=-1 is a solution of the linear equation 9kx+12ky=63.
2.
Find the point at which the equation 3x-2y=6 meets the x-axis.
3.
Express y in terms of x from the equation 3x+2y=8 and check whether the point (4,-2) lies on the line
4.
If x=2 and y=1 is the solution of the linear equation 2x+3y+k=0, find the value of k
5.
Give equations of two lines on the same plane which are intersecting at point(2,3).
6.
Give the geometrical representation of the equation 3x + 15 = 0 as an equation:
(i) in one variable
(ii) in two variables.
7.
Solve for x: \(3x+11+{x\over2}=-{7\over2}+18.\)What will be the graph of this equation?
8.
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.
9.
The cost of a note book is thrice the cost of a pen.Write a linear equation in two variables to represent this statement.Express it graphically.
10.
Given the point (1, 2), find the equation of a line on which it lies. How many such equations are there?Write the equation in the form ax + by + c = 0.
11.
Draw the graph of the linear equation y = m.x + c for m = 2 and c = 1. Read from the graph the value of y when x = \(3\over 2\)
12.
Given the point (1, 2), can you give the equation of a line on which it lies? How many such equations are there?
13.
Find three different solutions for the equation 6x-8y+32=0
14.
Express y in terms of x, it being given that 3x+y-9=0.Check whether the points (3,0) and (2, 2) lie on the equation
15.
Write the following as an equation in two variables:
5y=2
1.
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
2.
On x-axis, y co-ordinates is zero,
So put y=0 in 3x-2y=6, we get
3x-0=6
\(\Rightarrow x=\frac{6}{3}=2\)
3x-2y=6 meets the x-axis at (2,0)
3.
2y=8-3x
\(\Rightarrow \ y=\frac{8-3x}{2}\)
For x=4
\(y=
\frac{8-3\times4}{2}\)
\(=\frac{8-12}{2}=\frac{-4}{2}=-2\)
(4,-2) lies on the line.
4.
2x+3y+k=0
if x=2, and y=1 is the solution of the linear equation 2x+3y+k=0 then
2(2)+3(1)+k=0
k=-7
5.
The equation of two lines on the same plane which are intersecting at point (2,3) are:
x+y=5
y-x=1
6.
3x+15=0
\(\Rightarrow\) x=-5
(ii) Equation in one variable (Number line) : A point P at a distance of 5 units to left of 0 on the number
line.
(iii) In two variables (Cartesian plane) : A line AB parallel to y-axis at a distance of 5 units to the left of
y-axis.
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7.
x=1
8.
y=10+6(x-1) ⇒ y=4+6x
9.
y=3x
10.
x+y=3; infinitely many; x+y-3=0
11.
Ans: 4
12.
Here (1, 2) is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point (1, 2). One example of such a linear equation is x + y = 3. Others are y – x = 1, y = 2x, since they are also satisfied by the coordinates of the point (1, 2). In fact, there are infinitely many linear equations which are satisfied by the coordinates of the point (1, 2).
13.
(0,3), (4,6), (-4,0)
14.
y=9-3x; Yes; No
15.
0x+5y-2=0
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