Method of Substitution to Find the Solution of a Pair of Linear Equations

Q.

In the equation $ax+by+c=0$, if y= $\frac{(cx+d)}{b}$ and a = d, then what is the value of '$x$' ?

1. -1

2. -2

3. $\frac{(d+c)}{(a+c)}$

4. $\frac{(-d+c)}{(a+c)}$

Q. Given that $y=\frac{(cx+d)}{b}\text{, where}b\ne 0.$

$\text{If}ax+by+c=0\text{, where}(a+c)\ne 0$,
then what is the value of $x$ ?

1. $\frac{(d+c)}{(a+c)}$
2. $\frac{(-d-c)}{(a+c)}$
3. $\frac{(a+c)}{(d+c)}$
4. $\frac{(-d+c)}{(a+c)}$

Q. The sum of digits of a two digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number
[2 Marks]
[RD Sharma]
[Substitution Method]

Q.

Solving $\frac{5}{2+x}+\frac{1}{y-4}=2$; $\frac{6}{2+x}-\frac{3}{y-4}=1,$
we get

x = ___
y = ___

Q.

If $y=11–x$ and $2x–y=4$, we cannot find the value of $x$. Is this statement true or false?

1. True

2. False

Q.

For the equation, $x+3y=5$, $x$ in terms of $y$ can be written as____ and $y$ in terms of $x$ can be written as ______.

1. $x=5+y,y=5-3x$

2. $x=5–3y,y=\frac{(5-x)}{3}$

3. $x=5+3y,y=5+3x$

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

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 statements given below are the steps that need 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 the x if x and y are the two variables.

2) Substitute the x we got from step 2 in either of the equation to get y.

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

1. 1, 2, 3

2. 1, 3, 2

3. 2, 3, 1

4. 3, 2, 1

Q.

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

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

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

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

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

Q.

Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.

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

2. (1, 3)

3. $(\frac{4}{5},3)$

4. (1, 2)