Solving Simultaneous Linear Equation Using Method of Substitution

Q.

In the given equations $y=11–x$ and $2x–y=4$, the value of $x$ is 4.

1. True

2. False

Q. Question 1 (iii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{4}{x}+3y=14$
$\frac{3}{x}-4y=23$

Q. Question 3 (v)
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.

Solve the equations: $\frac{x}{a}$ + $\frac{y}{b}$ = 1 and the $xaxis$.

1. (-a, 0)

2. (b, 0)

3. (a, 0)

4. (-b, 0)

Q.

Question 1 (vii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\frac{15}{x+y}-\frac{5}{x-y}=-2$

Q.

Question 1 (i)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{1}{2x}+\frac{1}{3y}=2$
$\frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}$

Q.

Question 1 (vi)
Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy

Q.

Solve the following equations.

$\frac{3m}{5}+5=5$

Q.

Solve the equations y = x + 3 and 3x + y = 17.

1. (3, 4)

2. ( $\frac{5}{2}$, $\frac{13}{2}$)

3. ( $\frac{7}{2}$, $\frac{13}{2}$)

4. ( $\frac{-3}{2}$, $\frac{3}{2}$)

Q.

Solve $\frac{3x}{2}$ - $\frac{5y}{3}$ = -2; $\frac{x}{2}$ + $\frac{y}{2}$ = $\frac{13}{6}$

1. $x=\frac{51}{19},y=\frac{94}{57}$

2. $x=\frac{94}{57},y=\frac{51}{19}$

3. $x=\frac{117}{54},y=\frac{94}{57}$

4. $y=\frac{117}{54},x=\frac{94}{57}$

Q. We have two equations,
$\frac{1}{5}(x-2)=\frac{1}{4}(1-y)$

and

$26x+3y+4=0$

If we solve it using cross-multiplication, we use the following arrangement, after converting equations to the standard form



What are the values of A and B?

1. A = 13, B = 26
2. A = 4, B = 26
3. A = 5, B = 3
   
4. A = 3, B = 4

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. 87, 78
4. 41, 14

Q.

Question 1 (vi)
Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy

Q.

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per kilometer? How much does a person have to pay for travelling a distance of 25 km?

Q. Solve the following pair of equations by cross multiplication rule

1. $x=4$, $y=5$
2. $x=6$, $y=3$
3. $x=3$, $y=6$
4. $x=5$, $y=4$

Q.

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?

1. 2 m, 20 m

2. 2 m, 3 m

3. 26 m, 20 m

4. 56 m, 40 m

Q. Question 1 (iii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{4}{x}+3y=14$
$\frac{3}{x}-4y=23$

Q.

Solve the pair of linear equations using cross-multiplication method.

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

$26x+3y+4=0$

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

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

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

4. $x=2,y=3$

Q.

Question 1 (vii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\frac{15}{x+y}-\frac{5}{x-y}=-2$

Q. In substitution method of solving a pair of linear equations in 2 variables, first step is to solve one of the equations for x or y .

1. False
2. True

Q.

Find the solution of the given system of equations.

$\frac{x+y-8}{2}=\frac{x+2y-14}{8}=\frac{3x+y-12}{11}$

1. (1, -1)

2. (2, 6)

3. (2, 2)

4. (0, 1)

Q.

Solve the equations for $x$ and $y$.

$2x-3y=7$

$5x+y=9$

1. 3, 4

2. 2, -1

3. 2, 2

4. 3, -1

Q.

Solve the pair of linear equations using cross-multiplication method.

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

$26x+3y+4=0$

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

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

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

4. $x=2,y=3$

Q. We have two equations,
$\frac{1}{5}(x-2)=\frac{1}{4}(1-y)$

and

$26x+3y+4=0$

If we solve it using cross-multiplication, we use the following arrangement, after converting equations to the standard form



What are the values of A and B?

1. A = 13, B = 26
2. A = 4, B = 26
3. A = 3, B = 4
4. A = 5, B = 3
   

Q.

Question 1 (i)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{1}{2x}+\frac{1}{3y}=2$
$\frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}$

Q. Question 3 (v)
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.

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?

1. 2 m, 20 m

2. 26 m, 20 m

3. 56 m, 40 m

4. 2 m, 3 m

Q.

The given statements are the steps to be followed in the method of substitution in random order. Arrange them in correct order to solve two equations

1) Find the value of one variable, say y in terms of x if x and y are the two variables

2) Substitute the value of x obtained from previous step in either of the equation to find y.

3) Substitute y in the second equation and it will be reduced to an equation in x, find x

1. 1, 3, 2

2. 2, 3, 1

3. 3, 2, 1

4. 1, 2, 3

Q.

Which of the following option satisfies the given linear equation: 4x+3y = 5?

1. (1, 3)

2. (-1, 3)

3. (3, -1)

4. (-1, -3)