A system of three linear equations in three variables is consistent and independent. How many solutions to the system exist?
2 answers:
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<h2>Systems of Equations Word Problems</h2>
To solve these questions, we can translate key words into operations.
- <em>Older</em> = add
- <em>Less</em> <em>than</em> = subtract
We're given:
- Carlos' age is 5 less than 3 times his brother's age
- Carlos' age is 11 years higher than his brother's age
There are two variables present in this problem: Carlos' age and his brother's age.
- Let Carlos' age equal <em>x</em>
- Let his brother's age equal <em>y</em>
Translate the given information into equations:
- Carlos' age is 5 less than 3 times his brother's age
⇒ - Carlos' age is 11 years higher than his brother's age
⇒
We can solve for <em>y</em>, his brothers age, using substitution:
Now, solve for <em>x</em> by substituting <em>y</em> in either of the equations:
Therefore, Carlos is 19 years old.
<h2>Answer</h2>Carlos is 19 years old.