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 ,
[tex]\rm\implies x + y = 9 [/tex]
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
[tex]\rm\implies y = x+2[/tex]
Therefore the system of equations will be ,
Also when we will try to solve the equations we will get ,
[tex]\rm\implies x + y = 9 [/tex]
Put y = x + 2 , we have ,
[tex]\rm\implies x + x + 2= 9 [/tex]
Add the like terms ,
[tex]\rm\implies 2x +2 = 9 [/tex]
Transpose 2 to RHS ,
[tex]\rm\implies 2x = 9 -2 = 7[/tex]
Divide both sides by 2 ,
[tex]\rm\implies \boxed{\blue{\rm\quad x = 3.5\quad}}[/tex]
Similarly we will get the value of as ,
[tex]\rm\implies 3.5 + y = 9 [/tex]
Transpose 3.5 to RHS ,
[tex]\rm\implies y = 9 - 3.5 [/tex]
[tex]\rm\implies \boxed{\blue{\rm\quad y = 5.5\quad}}[/tex]
Therefore ,
[tex]\begin{cases} \rm x = 3.5 \\\\\rm y = 5.5 \end{cases}[/tex]
