Question

1. solve the system by substitution.

y = 6x + 11
2y - 4x = 14

Explanation:

Step1: Substitute y into the second equation

We know that \( y = 6x + 11 \), so substitute this expression for \( y \) into the equation \( 2y - 4x = 14 \). We get \( 2(6x + 11) - 4x = 14 \).

Step2: Simplify the left - hand side

First, distribute the 2 in \( 2(6x + 11) \): \( 12x+22 - 4x = 14 \). Then combine like terms: \( (12x - 4x)+22 = 14 \), which simplifies to \( 8x+22 = 14 \).

Step3: Solve for x

Subtract 22 from both sides of the equation: \( 8x=14 - 22 \), so \( 8x=-8 \). Then divide both sides by 8: \( x=\frac{-8}{8}=-1 \).

Step4: Solve for y

Substitute \( x = - 1 \) into the equation \( y = 6x+11 \). We get \( y=6\times(-1)+11=-6 + 11 = 5 \).

Answer:

The solution to the system of equations is \( x=-1 \) and \( y = 5 \), or the ordered pair \( (-1,5) \).