Question

use substitution to solve the system of equations.
y = 5x + 1
4x + y = 10

Explanation:

Step1: Substitute \( y = 5x + 1 \) into \( 4x + y = 10 \)

We replace \( y \) in the second equation with \( 5x + 1 \) from the first equation. So we get \( 4x+(5x + 1)=10 \).

Step2: Simplify and solve for \( x \)

First, remove the parentheses: \( 4x+5x + 1=10 \). Then combine like terms: \( 9x+1 = 10 \). Subtract 1 from both sides: \( 9x=10 - 1=9 \). Divide both sides by 9: \( x=\frac{9}{9} = 1 \).

Step3: Substitute \( x = 1 \) into \( y = 5x+1 \) to find \( y \)

Substitute \( x = 1 \) into the first equation: \( y=5\times1 + 1=5 + 1=6 \).

Answer:

The solution to the system of equations is \( x = 1 \) and \( y = 6 \) (or as an ordered pair \( (1,6) \)).