Question

solve each system of equations by substitut

1. \

$$\begin{cases} y = 3x + 19 \\\\ y = 5x + 33 \\end{cases}$$

Explanation:

Step1: Substitute \( y \) from first equation into second equation.

Since \( y = 3x + 19 \) and \( y = 5x + 33 \), we set \( 3x + 19 = 5x + 33 \).

Step2: Solve for \( x \).

Subtract \( 3x \) from both sides: \( 19 = 2x + 33 \).
Subtract 33 from both sides: \( -14 = 2x \).
Divide by 2: \( x = -7 \).

Step3: Substitute \( x = -7 \) into first equation to find \( y \).

\( y = 3(-7) + 19 = -21 + 19 = -2 \).

Answer:

The solution to the system is \( x = -7 \), \( y = -2 \) (or as an ordered pair \( (-7, -2) \)).