1 Marks Question

Question 11 Mark

On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equation is consistent, or inconsistent: 5x - 3y = 11; -10x + 6y = -22

Answer

Formulation: Let the number of girls be x and the number of boys be y.
It is given that total ten students took part in the quiz.
$\therefore$ Number of girls+ Number of boys = 10
i.e. x + y =10
It is also given that the number of girls is 4 more than the number of boys.
$\therefore$ Number of girls= Number of boys + 4
i.e. x = y+4
or, x-y = 4
Thus, the algebraic representation of the given situation is
x + y=10 ........(i)
x - y =4 ..........(ii)
Add (i) and (ii) we get
x + y + x - y = 10 + 4
2x = 14
x = 7
Put x = 7 in (i)
x + y = 10
7 + y = 10
y = 10 -7
y = 3
So, value of x = 7 and y = 3
Graphical Representation: Now putting y = 0 in x + y = 10, we get
x = 10. Similarly, by putting x = 0 in x + y = 10, we get y = 10.
Thus, two solution of equation (i) are:

x	10	0
y	0	10

Similarly, two solutions of equation (ii) are:
putting y = 0 in x - y = 4, we get
x = 4. Similarly, by putting x = 0 in x + y = 10, we get y = -4.

x	4	0
y	0	-4

Now, we plot the points A (10, 0), B (0, 10), P (4, 0) and Q (0, -4) corresponding to these solutions on the graph paper and draw the lines AB and PQ representing the equations x + y = 10 and x - y - 4 as shown in Fig.

We observe that the two lines representing the two equations are intersecting at the point (7, 3).

View full question & answer→

Question 21 Mark

On comparing the ratios $\frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } \text { and } \frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equations are consistent, or inconsistent: $\frac { 4 } { 3 } x$ + 2y = 8; 2x + 3y = 12.

Answer

Given equations are:
$\frac{4}{3} x+2 y=8 ; 2 x+3 y=12$
Compare equation $\frac{4}{3} x+2 y=8$ with $a _1 x + b _1 y + c _1=0$ and $2 x +3 y =12$ with $a_2 x+b_2 y+c_2=0$, We get, $a_1=\frac{4}{3}, a_1=\frac{4}{3}, b_1=2, c_1=-8, a_2=2, b_2=3, c_2=-12$ $\frac{a_1}{a_2}=\frac{\frac{4}{3}}{2}=\frac{2}{3}, \frac{b_1}{b_2}=\frac{2}{3}$ and $\frac{c_1}{c_2}=\frac{8}{12}=\frac{2}{3}$ Here $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Therefore, the lines have infinitely many solutions.
Hence, they are consistent.

View full question & answer→

Question 31 Mark

Use elimination method to find all possible solutions of the following pair of linear equations:
2x + 3y = 8 ...(1)
4x + 6y = 7 ...(2)

Answer

Step 1: Multiply equation (i) by 2 and equation (ii) by 1 to make the coefficients of x equal. Then we get the equations as :
4x + 6y = 16 ...(iii)
4x + 6y = 7 ...(iv)
Step 2: Subtracting equation (iv) from equation (iii),we get
(4x - 4x) + (6y - 6y) = 16 - 7
i.e., 0 = 9, which is a false statement. Therefore, the given pair of equations has no solution.

View full question & answer→

Maths 1 Marks Question

Take a timed test