Question

3. The sum of x and y is 9. The value of y is two more than the value of x. Write a system of equations to model this.

Answer 1

Answer:

x + y = 9

y = x + 2

Step-by-step explanation:

We need to write a system of equations to represent the given situation . The statements are ,

Statement 1:- The sum of x and y is 9.

Mathematically , we can write it as ,

$\rm\implies x + y = 9$

Statement 2:- The value of y is two more than the value of x.

This simply means that y equals to 2 + x , that is

$\rm\implies y = x+2$

Therefore the system of equations will be ,

• x + y = 9
• y = x + 2

Also when we will try to solve the equations we will get ,

$\rm\implies x + y = 9$

Put y = x + 2 , we have ,

$\rm\implies x + x + 2= 9$

Add the like terms ,

$\rm\implies 2x +2 = 9$

Transpose 2 to RHS ,

$\rm\implies 2x = 9 -2 = 7$

Divide both sides by 2 ,

$\rm\implies \boxed{\blue{\rm\quad x = 3.5\quad}}$

Similarly we will get the value of as ,

$\rm\implies 3.5 + y = 9$

Transpose 3.5 to RHS ,

$\rm\implies y = 9 - 3.5$

$\rm\implies \boxed{\blue{\rm\quad y = 5.5\quad}}$

Therefore ,

$\begin{cases} \rm x = 3.5 \\\\\rm y = 5.5 \end{cases}$