2.5 CW Systems of Equations: Slope-Intercept Form and Substitution Practice

For each question below, you are given a system of equations in slope-intercept form (y = mx + b). For each system:

1. List the slope (m) and y-intercept (b) for each equation.
2. Determine if the system is:

• Consistent dependent (infinitely many solutions)
• Consistent independent (exactly one solution)
• Inconsistent (no solution)

1. Explain why the system falls into your chosen category, referencing the slopes and y-intercepts.
2. Show all your work and reasoning for full credit.

For the second section, solve each system using substitution. No fractions will appear in any answer.

/** For each system, follow the instructions in the introduction. **/

System 1: y = 2x + 3 y = 2x + 3

List the slope and y-intercept for each equation, determine the type of system, and explain your reasoning.

System 2: y = -x + 4 y = -x - 2

List the slope and y-intercept for each equation, determine the type of system, and explain your reasoning.

System 3: y = 3x - 1 y = -3x + 5

List the slope and y-intercept for each equation, determine the type of system, and explain your reasoning.

System 4: y = x + 2 y = x - 5

List the slope and y-intercept for each equation, determine the type of system, and explain your reasoning.

Solve each system of equations by substitution. Show all your work. All answers will be integers (no fractions).

System 1: y = 2x + 1 x + y = 7

Solve the system using substitution. Show all your work.

System 2: y = x - 3 2x + y = 11

Solve the system using substitution. Show all your work.

System 3: y = -x + 6 x + y = 2

Solve the system using substitution. Show all your work.

System 4: y = 4x x + y = 10

Solve the system using substitution. Show all your work.