Sure, let's break down the statement: "Twice the age of the father is equal to seven times the age of the son" and convert it into a linear equation in two variables.
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the age of the father.
- Let [tex]\( y \)[/tex] represent the age of the son.
2. Translate the Statement into a Mathematical Equation:
- "Twice the age of the father" can be expressed as [tex]\( 2x \)[/tex].
- "Seven times the age of the son" can be expressed as [tex]\( 7y \)[/tex].
- According to the problem, these two expressions are equal.
3. Write the Equation:
- So we have [tex]\( 2x = 7y \)[/tex].
4. Rearrange into Standard Linear Equation Form [tex]\( Ax + By = C \)[/tex]:
- To do this, we can rearrange the equation [tex]\( 2x = 7y \)[/tex].
- Subtract [tex]\( 7y \)[/tex] from both sides to get [tex]\( 2x - 7y = 0 \)[/tex].
Thus, the linear equation in two variables that corresponds to the statement "Twice the age of the father is equal to seven times the age of the son" is:
[tex]\[ 2x - 7y = 0 \][/tex]
This is now in the standard linear form [tex]\( Ax + By = C \)[/tex], where [tex]\( A = 2 \)[/tex], [tex]\( B = -7 \)[/tex], and [tex]\( C = 0 \)[/tex].
