The value of $x$ depends on the value of $y$. So the dependent variable is x and the independent variable is y.

Sum of the coefficients of dependent and independent variable $=(10+1)=11$

The sum of numbers $p$ and $4$ is $15$.

Each part: 1 Mark
(a) $5z+27=3z+33$
$\Rightarrow 5z-3z=33-27$
$\Rightarrow 2z=6$
$\Rightarrow z=3$
$\therefore z=3.$
(b) $7x+14=34-3x$
$\Rightarrow 7x+14=34-3x$
$\Rightarrow 7x+3x=34-14$
$\Rightarrow 10x=20$
$\therefore x=\frac{20}{10}=2$

Solution: 1 Mark each
(a) $4x+10=20$
Dividing all the terms by 2, we get
$2x+5=10$
$\Rightarrow 2x=5$
$\Rightarrow x=\frac{5}{2}$
$\Rightarrow x=2.5$
(b) Let the number of marbles Parmeet has = $m$
No. of marble Irfan has in terms of $m$ = $5m+7$
Given that Irfan has 37 marbles, the equation so formed will be
$\Rightarrow 5m+7=37$

Definition of Each: 1 Mark
A combination of variables and constants connected by the arithmetic operators such as addition(+), subtraction(-), multiplication(x) and division(÷) is called an expression.
e.g. $(3x-7)$ is an expression.
An equation is a mathematical statement wherein two expressions are set equal to each other.
e.g. $(3x-7)=65$ is an equation.
       $(3x-7)=6y+8$ is an equation.

(a) 1 Mark
(b) Framing the equation: 1 Mark
     Solution: 1 Mark
(a) Since it is a triangle, the perimeter of a triangle is equal to the sum of all the sides of the triangle.
     So, $x+(x+3)+41=86$
     $\Rightarrow 2x+44=86$
     $\Rightarrow 2x=42$
 
    $\Rightarrow x=21$.
(b) Let the base angle be $b^{\circ }$
     Let the vertex angle be $a^{\circ }$
    In an isosceles triangle base angles are equal.
    $\therefore a^{\circ }+b^{\circ }+b^{\circ }={180}^{\circ }$
    $2b^{\circ }+b^{\circ }+b^{\circ }={180}^{\circ }\Rightarrow$ Given that vertex angle is twice the base angle.
    $\therefore 4b^{\circ }={180}^{\circ }$
    $b^{\circ }=(\frac{180}{4}{)}^{\circ }$
    $b^{\circ }={45}^{\circ }$

Each part: 1 Mark
The equations are as follows:
a) Let the number be $x$
    $\frac{x}{3}+5=8$.
    $\frac{x}{3}=8-5$.
    $\frac{x}{3}=3$.
    $x=9$.
b) Let the number be $x$
    $(4\times x)+8=2\times x$.
     $4x+8=2x$.
     $4x-2x=-8$.
     $2x=-8$.
     $x=-4$
c) $(3\times x)-11=31$.
    $3x-11=31$.
    $3x=31+11$.
    $3x=42$.
    $x=14$.