Elimination Method to Find the Solution of Pair of Linear Equations

Q.

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction. [3 MARKS]

Q. A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If 5 is subtracted from the numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

1. $\frac{-7}{9}$
2. $\frac{7}{10}$
3. $\frac{-7}{10}$
4. $\frac{7}{9}$

Q. Sum of two numbers is 44 and their difference is 4. Find the greater number among the two.

1. 24
2. 28
3. 20
4. 16

Q. Solve the following pair of equations:

$7x-8y=-12$

$-4x+2y=3$

1. $x=0,y=0$
2. $x=0,y=\frac{3}{2}$
3. $x=\frac{5}{2},y=4$
4. $x=6,y=\frac{1}{2}$

Q.

A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction. [3 MARKS]

Q. A fraction becomes $\frac{4}{5}$ if 4 is added to both numerator and denominator. If, however, 5 is subtracted from numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

1. $\frac{7}{9}$
2. None of the above
3. $\frac{8}{11}$
4. $\frac{-8}{11}$

Q. If the sum and difference of two numbers is 34 and 20 respectively, then the product of those numbers are ___.

1. 189
2. 289
3. 199
4. 249

Q.

Question 7

In the following question out of the four options only one is correct, write the correct answer.

If a and b are positive integers, then the solution of the equation ax=b has to be always:

(a) positive

(b) negative

(c) one

(d) zero

Q. Solve:
$\frac{1}{3x}+\frac{1}{5y}=1$;
$\frac{1}{5x}+\frac{1}{3y}=1\frac{2}{15}$

1. $x=\frac{21}{3},y=\frac{6}{5}$
2. $x=\frac{2}{3},y=\frac{2}{5}$
3. $x=\frac{7}{2},y=-\frac{8}{3}$
4. $x=-\frac{8}{5},y=\frac{9}{4}$

Q.

The larger of two supplementary angles exceeds the smaller by 58°, then find the angles.

Q.

Solve for y if the pair of linear equations are

$\frac{5}{(x-2)}=\frac{4}{(1-y)}and$

$26x+3y+4=0$

1. 3

Q. Solve the following pair of equations:
$\frac{1}{x}+\frac{3}{y}=1$
$\frac{6}{x}-\frac{12}{y}=2$
(Where $x\ne 0,y\ne 0)$

1. $x=\frac{3}{5},y=\frac{7}{3}$
   
2. $x=\frac{5}{3},y=\frac{15}{2}$
3. $x=3,y=11$
4. $x=4,y=9$

Q. If $2$ is added to the numerator of a fraction, it reduces to $\frac{1}{2}$ and if $1$ is subtracted from denominator, it reduces to $\frac{1}{3}$. Find the fraction.

Q. Solve the following system of equation:
$\frac{1}{2x}-\frac{1}{y}=-1$
$\frac{1}{x}+\frac{1}{2y}=8$ , where x $\ne$ 0, y $\ne$ 0.

Q. In the elimination method of solving two linear equations in 2 variables, we always add the equations to eliminate any one variable.

1. False
2. True

Q. Half the perimeter of a rectangular garden, whose length is 8 m more than its width, is 40 m. Find the dimensions of the garden.

1. Length = 24m, Breadth = 16m
2. Length = 20m, Breadth = 18m
3. Length = 24m, Breadth = 20m
4. Length = 40m, Breadth = 36m

Q. The sum of a two-digit number and the number obtained by reversing the order of its digits is 121. Also, the difference of the units digit and the tens digit is 3. Then, the numbers are

1. 62, 26
2. 47, 74
3. 41, 14
4. 87, 78

Q. Solve :
$x+y=2xy$
$x-y=6xy$

1. $x=-\frac{1}{2}$ and $y=\frac{1}{7}$
2. $x=-\frac{1}{2}$ and $y=\frac{1}{4}$
3. $x=-\frac{1}{2}$ and $y=\frac{1}{2}$
4. $x=-\frac{1}{2}$ and $y=\frac{1}{5}$

Q.

The time taken to travel 30 km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11 km then the total time taken is 11 hours more than earlier. Find the speed of the stream.

1. 4 km/hr

2. 7 km/hr

3. 3 km/hr

4. 6 km/hr

Q. Solve each of the following systems of equations by using the method of cross multiplication:
$1/x+1/y=7$
$2/x+3/y=17(x\ne 0andy\ne 0)$

Q.

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction. [3 MARKS]

Q. Solve: $\frac{1}{2x}-\frac{1}{y}=-1;\frac{1}{x}+\frac{1}{2y}=8$.

Q. Solve the following pair of equations:

$7x-8y=-12$

$-4x+2y=3$

1. $x=0,y=0$
2. $x=0,y=\frac{3}{2}$
3. $x=\frac{5}{2},y=4$
4. $x=6,y=\frac{1}{2}$

Q. Solve the following systems of equations:
$\frac{7x-2}{xy}=5$
$\frac{8x+7y}{xy}=15$

Q.

If point $P(a,b)$ lies on the straight line $3x+2y-16=0$ and the point $Q(b,a)$ lies on the straight line $4x-y-5=0$. The equation of the line $PQ$ is

1. $x-y=5$
2. $x+y=5$
3. $x+y=-5$
4. $x-y=-5$

Q. A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If, however, 5 is subtracted from numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

1. $\frac{-7}{9}$
2. $\frac{7}{10}$
3. $\frac{-7}{10}$
4. $\frac{7}{9}$

Q. Solve:
$2x-9y=9,5x+2y=27$

1. $x=\frac{19}{49},y=\frac{26}{49}$
2. $x=\frac{261}{49},y=\frac{9}{49}$
3. $x=\frac{9}{49},y=\frac{261}{49}$
4. $x=\frac{49}{261},y=\frac{49}{149}$

Q.

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

1. $5km/hr$

2. $9km/hr$

3. $\frac{9}{7}km/hr$

4. $\frac{10}{3}km/hr$

Q. Sum of two numbers is 35 and their difference is 13. Find the greater number.

1. 21
2. 26
3. 25
4. 24

Q. The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

1. ₹120, ₹48/hr
2. ₹200, ₹48/hr
3. ₹120, ₹100/hr
4. ₹200, ₹120/hr