Question

solve the system by substitution.
$4x + y = 42$
$y = x + 7$

Explanation:

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

Substitute \( y \) in the first equation with \( x + 7 \), we get \( 4x+(x + 7)=42 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( 4x+x + 7=42\), which is \( 5x+7 = 42 \).
Subtract 7 from both sides: \( 5x=42 - 7=35 \).
Divide both sides by 5: \( x=\frac{35}{5}=7 \).

Step3: Substitute \( x = 7 \) into \( y=x + 7 \) to find \( y \)

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

Answer:

The solution of the system is \( x = 7 \) and \( y = 14 \)