Solving Equations Using Method of Elimination

Q.

Solve the following equation: $17+6p=9$

Q. Express $0.6+0.4\overline{7}+0.\overline{7}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Q. Arvind and Vinod have some erasers . Arvind said to Vinod , if you give me 10 erasers, I will have twice the erasers left with you . Represent the solution as linear equations 2 variables

Q.

Solving the following pair of equations using elimination method, gives x = a and y = -b
$\frac{x}{a}-\frac{y}{b}=0$
$ax+by=a^2+b^2$

1. True

2. False

Q. Solve: 3x + 4y = 10, 2x − 2y = 2 by the method of elimination.

Q.

Simultaneous linear equations

1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number.

2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.

Q. 29. solve the following pair of linear equations by the substitution method 0.2x+0.3y=1.3

Q.

The solution of the following pair of equations:

2x + 3y = 11 and 2x - 4y = -24 is ___.

Write your answer in the form (x, y)

1. (-2, 5)

2. (3, 5)

3. (2, 5)

4. (5, 3)

Q. A fraction is 9/11, if 2 is added to both the numerator and denominator. The numerator and denominator of the fraction are x and y respectively. Write a linear equation for this information and draw a graph

Q.

Find the unique solution for the pair of linear equations: x + 2y = 5 and 7x + 3y = 13.

1. (1, 2)

2. (2, 1)

3. (3, 1)

4. (1, 3)

Q.

We have two equations
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
In the above equations, to eliminate the coefficients of x, what has to be done?

1. Multiply equation (1) by 6 and equation (2) by 4

2. Multiply equation (1) by 3 and equation (2) by 5

3. Multiply equation (1) by 5 and equation (2) by 3

4. None

Q. The pairs of linear equations which have the unique solution x = 2, y = –3 are

i. x + y = –1 ; 2x + 3y = –5
ii. 2x + 5y = –11 ; 4x + 8y = –22
iii. 2x – y = 1 ; 3x + 2y = 0
iv. x – 4y –14 = 0 ; 5x – y – 13 = 0

1. i and ii
2. ii and iii
3. iii and iv
4. i and iv

Q.

Simplify the expressions.
$4b-24+19$

Q.

Oral Questions:

What is transposition?

Q.

Solve the following pair of equations:
$8v-3u=5uv$
$6v-5u=-2uv$

1. $u=0,v=0$

2. $u=\frac{22}{31},v=\frac{11}{23}$

3. Both A and B

4. None of these

Q.

Find the values of $x$ and $y$ that satisfy the below given pair of equations, where $x\ne 0\&y\ne 0$.

$\frac{2}{x}+\frac{3}{y}=13$

$\frac{5}{x}-\frac{4}{y}=-2$

1. $x=\frac{1}{2},y=\frac{1}{3}$

2. $x=\frac{1}{3},y=\frac{1}{2}$

3. $x=2,y=3$

4. $x=3,y=2$

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.

Select the correct order for solving a pair of linear equations in two variables by elimination method.

i) Add or subtract one equation from the other so that one variable gets eliminated.

ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal.

iii) Substitute the obtained value in either of the original equations to get the value of the other variable.

iv) Solve the equation in one variable thus obtained to get its value.

1. (i), (iv), (ii), (iii)

2. (ii), (i), (iii), (iv)

3. (i), (iv), (iii), (ii)

4. (ii), (i), (iv), (iii)

Q. $2x-3y=-14$
$3x-2y=-6$
If $(x,y)$ is a solution to the system of equations above, what is the value of $xy$?

1. $-20$
2. $12$
3. $8$
4. $-8$

Q. If, 2x - y = 2 and x - 2y = 1 then.

1. x = 1 and y = 0
2. x = 1 and y = 1
3. x = 0 and y = 1
4. x = 2 and y = 2

Q. If 2x + y = 4 and 3x + y = 5, then the common solution for these two equations is .

[Use elimination method to solve]

1. x = 1 and y = 2
2. x = 2 and y = 1
3. x = 0 and y = 4
4. x = 2 and y = 0

Q.

Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(Where $x>0,y>0)$

1. $x=9,y=4$

2. $x=4,y=9$

3. $x=3,y=2$

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

Q. Solve the following systems of equations.
$x^2+y^2-xy=13,x+y-\sqrt{xy}=3$

Q.

Solve the following pairs 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. Find two numbers such that the sum of twice the first and thrice the second is $89$ and four times the first exceeds five times the second by $13$

1. The required numbers are $10$ and $19$
2. The required numbers are $26$ and $11$
3. The required numbers are $22$ and $15$
4. The required numbers are $4$ and $21$

Q. If y $\alpha$$\frac{1}{x^3}$ and y = 4 when x =3. Find y when x = 4.

Q. y a$\sqrt{x}$ and y = 8 when x = 4 then, find

(i) The value of y when x = 9
(ii) The value of x when y = 144

Q. For the equations $\frac{2}{x}+\frac{3}{y}=13$ and
$\frac{5}{x}-\frac{4}{y}=-2$ where $x\ne 0\&y\ne 0$, the value of

1. $x=\frac{1}{3}$
2. $y=\frac{1}{3}$
3. $x=\frac{1}{4}$
4. $y=\frac{1}{3}$

Q.

Solution for the following pair of linear equations is:
2x + 4y = 8
4x + 8y = 0

1. Infinite solutions

2. (8, 0)

3. No solution

4. (0, 16)

Q.

Find the unique solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13.