Question

1. determine whether the system of linear equations below has one solution, infinitely many solutions, or no solution. if the system has a solution, find the solution and write it as an ordered pair (x, y).

32x - y = 19
y = 32x - 4

1. determine whether the system of linear equations below has one solution, infinitely many solutions, or no solution. if the system has a solution, find the solution and write it as an ordered pair (x, y).

x + 2y = 7
y = 2x - 4

1. determine whether the system of linear equations below has one solution, infinitely many solutions, or no solution. if the system has a solution, find the solution and write it as an ordered pair (x, y)

-3x + 3y = -3
y = -2x + 2

Explanation:

Problem 3

Step1: Substitute \( y = 32x - 4 \) into \( 32x - y = 19 \)

Substitute \( y \) in the first equation: \( 32x - (32x - 4) = 19 \)

Step2: Simplify the equation

Simplify: \( 32x - 32x + 4 = 19 \) → \( 4 = 19 \) (which is false)

Step1: Substitute \( y = 2x - 4 \) into \( x + 2y = 7 \)

Substitute \( y \) in the first equation: \( x + 2(2x - 4) = 7 \)

Step2: Expand and simplify

Expand: \( x + 4x - 8 = 7 \) → \( 5x - 8 = 7 \)

Step3: Solve for \( x \)

Add 8 to both sides: \( 5x = 15 \) → \( x = 3 \)

Step4: Find \( y \) using \( y = 2x - 4 \)

Substitute \( x = 3 \): \( y = 2(3) - 4 = 2 \)

Step1: Substitute \( y = -2x + 2 \) into \( -3x + 3y = -3 \)

Substitute \( y \) in the first equation: \( -3x + 3(-2x + 2) = -3 \)

Step2: Expand and simplify

Expand: \( -3x - 6x + 6 = -3 \) → \( -9x + 6 = -3 \)

Step3: Solve for \( x \)

Subtract 6: \( -9x = -9 \) → \( x = 1 \)

Step4: Find \( y \) using \( y = -2x + 2 \)

Substitute \( x = 1 \): \( y = -2(1) + 2 = 0 \)

Answer:

No solution

Problem 4