Solving Equations Using Method of Substitution

Q. Students of a class are made to stand in complete rows. If one student is extra in a row there would be 2 rows less. If 1 student is less in a row there would be 3 rows more . find the number of students in the class.

please solve it using simultaneous Linear Equations

Q.

1) X/6+y/15=4

X/3-y/12=19/4

Solved it by elimination of substitution

Q. 54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

1. 34
2. 32
3. 30
4. 24

Q. The sum of a two-digit number and the number obtained by reversing the digits is 88. If the digits of the number differ by 2, find the numbers.

1. 53, 35
2. 71, 17
3. 44, 44
4. 36, 63

Q.

Solve x + y = 10 ;x - y = 2, by the method of substitution.

1. x = 6 , y = -4

2. x = 4 , y = 6

3. x = 6 , y = 4

4. x = -6 , y = 4

Q. For what value of k will the equations x + 2y + 7 = 0, 2x + ky + 14 = 0 represents coincident lines?

1. 9
2. 6
3. 4
4. 3

Q.

If the cost of $6$ cans of juice is $Rs.210$, then what will be the cost of $4$ cans of juice ?

Q.

Solve the following system of equations using elimination method:​
$2x+7y=10$​
$3x+y=6$

1. $\frac{32}{19},\frac{18}{19}$
2. $\frac{-3}{5},\frac{9}{5}$
3. $\frac{11}{25},\frac{9}{25}$
4. $\frac{12}{19},\frac{-1}{19}$

Q.

If $x=\frac{4\sqrt{6}}{\sqrt{2}+\sqrt{3}}$. Find the value of $\frac{x+2\sqrt{2}}{x-2\sqrt{2}}+\frac{x+2\sqrt{3}}{x-2\sqrt{3}}$, using the properties of proportion.

1. 3

2. 2

3. 1

4. 0

Q. a√a + b√b = 183
a√b + b√a = 182
Find 9/5(a+b)
Please show the steps also.

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

1. 3, 2
2. 6, 3
3. 4, 7
4. 7, 8

Q. Question 2
Write four solutions for each of the following equations:
$\left(i\right)2x+y=7\left(ii\right)\pi x+y=9\left(iii\right)x=4y$

Q.

Solve for x and y using substitution method:

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(Given: $x\ne 0andy\ne 0)$

1. $x=\frac{1}{6},y=\frac{1}{4}$

2. $x=\frac{1}{8},y=\frac{1}{3}$

3. $x=\frac{1}{7},y=\frac{1}{2}$

4. $x=\frac{3}{4},y=\frac{5}{4}$

Q.

Prove that (x+y)³ - (x-y)³ - 6y(x² - y² ) = 8y³

Q.

3x-5y=4 9y-2y =7 by substitution method

Q. Question 2 (i)
Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Q. A person rows downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man's speed of rowing in still water and the speed of the current.

Q.

Solve: $2x+y=-4,3y=5x-1$

By Substitution method

Q.

How do you solve an equation using substitution$?$

Q. $x-3y=-8$

Q.

Classify True or False:

$xy=3$ is a linear equation in two variables.

1. True
2. False

Q. If x=a⅓-a^-⅓, then find x³-3x-a

Q.

If (3, 2) is a solution of the equation $4x-ky=10$, then find the value of $k$.

1. 0

2. 2

3. 1

4. 3

Q.

What is the solution of the equation $3x+7y=30$ if $x=y$?

1. $(1,1)$

2. $(2,2)$

3. $(3,3)$

4. $(4,4)$

Q. Question 1 (vi)
Solve the following pair of linear equations by the substitution method.
$\frac{3x}{2}-\frac{5y}{3}=-2;\frac{x}{3}+\frac{y}{2}=\frac{13}{6}$

Q.

Form the pair of linear equations for the following problems and find their solution by substitution method:

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.

Q.

If p(x) = 2x³ + ax² − 7x + b and we want p(1) = 3 and p(2) = 19 what should be a and b?

Q. Question 6 (ii)
Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(ii) Parallel lines

Q.

Question 1 (iii)
Solve the following pair of linear equations by the elimination method and the substitution method:
3x - 5y - 4 = 0 and 9x = 2y + 7

Q.

Question 9 (i)
Solve the following pair of equations
$x+y=3.3,\frac{0.6}{3x-2y}=-1\text{where}3x-2y\ne 0$.