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14 votes
14 votes
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

User Geoaxis
by
2.3k points

1 Answer

15 votes
15 votes

Answer:

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}

User Dan Stocker
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