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.

fa+y=9
x = y + 2
x - y = 9
y + 2
x-y-9
x = y + 2
X +y=9
y = x + 2

Answer 1

x + y = 9

y = x + 2

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}`