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Three times a number minus a different number is equal to -3. The sum of the numbers is 11. What are the two numbers?
Define Variables:
Write a system and solve:
Solution sentence:

That is how it was worded if you could help me with this problem I would be so grateful!

Respuesta :

Eddie1Wan

Step-by-step explanation:

Define variables: let the numbers be x and y

Write a system: 3x-y=-3

x+y=11

Solve: Add both numbers to eliminate y

4x=8

x=2

Plug x=2 into the second equation

2+y=11

y=11-2=9

Solution sentence: the values are 2 and 9

Answer:

  • 2 and 9

[tex] \\ [/tex]

Step-by-step explanation:

It is given that, three times a number minus a different number is equal to -3 and the sum of the numbers is 11 and we are to find the numbers.

[tex] \\ [/tex]

  • Let us assume the numbers as a and b .

Three times a minus a different number is equal to -3 :

[tex]{\longrightarrow \pmb{\sf {\qquad 3a-b=-3 \:...... \: (i)}}} \\ \\[/tex]

The sum of the numbers is 11.

[tex]{\longrightarrow \pmb{\sf {\qquad a + b=-11 \:...... \: (ii)}}} \\ \\[/tex]

Adding equation (i) and (ii) :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad 3a-b + (a + b)=-3 + 11 }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad 3a \: \: \cancel{-b }+ a + \cancel b=8 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad 4a =8 }}} \\ \\[/tex]

Dividing both sides by 4 :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad \frac{4a}{4} = \frac{8}{4} }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad a =2 }}} \\ \\[/tex]

Now, Substituting the value of a in equation (ii)

[tex]{\longrightarrow \pmb{\sf {\qquad a + b=11 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad 2 + b=11 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad b=11 - 2 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad b=9 }}} \\ \\[/tex]

Therefore,

  • The two numbers are 2 and 9

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