Question

solve the system by substitution.
\\(4x + y = 42\\)
\\(y = x + 7\\)

Explanation:

Step1: Substitute \( y = x + 7 \) into \( 4x + y = 42 \)

We get \( 4x + (x + 7) = 42 \).

Step2: Simplify the equation

Combine like terms: \( 4x + x + 7 = 42 \) which becomes \( 5x + 7 = 42 \).
Subtract 7 from both sides: \( 5x = 42 - 7 = 35 \).

Step3: Solve for \( x \)

Divide both sides by 5: \( x = \frac{35}{5} = 7 \).

Step4: Solve for \( y \)

Substitute \( x = 7 \) into \( y = x + 7 \), so \( y = 7 + 7 = 14 \).

Answer:

The solution to the system is \( x = 7 \) and \( y = 14 \), or the ordered pair \( (7, 14) \).