Substitution Method of finding solution of a pair of LE

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.

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

x = ___
y = ___

Q.

Solve and find value of y.

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

1. $y=\frac{117}{54}$

2. $y=\frac{51}{19}$

3. $y=\frac{57}{19}$

4. $y=\frac{94}{57}$

Q. In a two-digit number, the units digit is twice the ten's digit. Also, if 27 is added to the number, the digits interchange their places. Find the number.

1. 40
2. 36
3. 52
4. 28

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)

Q.

Measure of one of the angles of a parallelogram is twice the measure of its adjacent angle. Then angles of the parallelogram are

1. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$

2. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$

3. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$

4. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$

Q. What is the solution for the following pair of linear equations?

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

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

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

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

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.

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. 56 m, 40 m

2. 26 m, 20 m

3. 2 m, 20 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.

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.

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